Triangle Geometry 3

Question 1 of 4

Find the value of

a

$a$

$a =$ $a=$ (40)°

Incorrect

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Supplementary angles are when two angles have a sum of

180 ° .

$180°.$ Typically, these angles lie on a straight line.

An Isosceles Triangle has two congruent sides (the two sides with dashes) and the two base angles are equal.

The sum of the interior angles in a triangle is $180 °$ $180°$

To solve for

a

$a$ , find the measure of the missing interior angles, add it to

a

$a$ and set their sum to

180 °

$180°$ .

First, we can see from the diagram that the exterior angle

110 °

$110°$ and the interior angle

b

$b$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

a

$a$ .

$b + 110$ $b+110$	$=$ $=$	$180$ $180$
$b + 110$ $b+110$ $- 110$ $-110$	$=$ $=$	$180$ $180$ $- 110$ $-110$	Subtract $110$ $110$ from both sides
$b$ $b$	$=$ $=$	$70 °$ $70°$

Next, since the base angles in an isosceles triangle are equal, $c$ $c$ is equal to

70 ˚

$70˚$

c

$c$

=

$=$

70

$70$

Finally, since the interior angles of a triangle add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for

b

$b$ .

$a + b + c$ $a+b+c$	$=$ $=$	$180$ $180$
$a + 70 + 70$ $a+70+70$	$=$ $=$	$180$ $180$	Plug in the known values
$a + 140$ $a+140$	$=$ $=$	$180$ $180$	Simplify
$a + 140$ $a+140$ $- 140$ $-140$	$=$ $=$	$180$ $180$ $- 140$ $-140$	Subtract $140$ $140$ from both sides
$a$ $a$	$=$ $=$	$40 °$ $40°$

∠ a = 40 °

$/_ a=40°$

Question 2 of 4

Find the value of

x

$x$

$x =$ $x=$ (150)°

Incorrect

Supplementary angles are when two angles have a sum of

180 ° .

$180°.$ Typically, these angles lie on a straight line.

The sum of the interior angles in a triangle is $180 °$ $180°$

To solve for

x

$x$ , find the supplementary angle of

z

$z$ .

First, we can see from the diagram that the exterior angle

100 °

$100°$ and the interior angle

y

$y$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

y

$y$ .

$y + 100$ $y+100$	$=$ $=$	$180$ $180$
$y + 100$ $y+100$ $- 100$ $-100$	$=$ $=$	$180$ $180$ $- 100$ $-100$	Subtract $100$ $100$ from both sides
$y$ $y$	$=$ $=$	$80 °$ $80°$

Next, since the interior angles of a triangle add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for

z

$z$ .

$y + z + 80$ $y+z+80$	$=$ $=$	$180$ $180$
$80 + z + 70$ $80+z+70$	$=$ $=$	$180$ $180$	Plug in the known values
$z + 150$ $z+150$	$=$ $=$	$180$ $180$	Simplify
$z + 150$ $z+150$ $- 150$ $-150$	$=$ $=$	$180$ $180$ $- 150$ $-150$	Subtract $150$ $150$ from both sides
$z$ $z$	$=$ $=$	$30 °$ $30°$

Finally, we can see from the diagram that the exterior angle

x

$x$ and the interior angle

z

$z$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

x

$x$ .

$x + z$ $x+z$	$=$ $=$	$180$ $180$
$x + 30$ $x+30$	$=$ $=$	$180$ $180$	Plug in the known values
$x + 30$ $x+30$ $- 30$ $-30$	$=$ $=$	$180$ $180$ $- 30$ $-30$	Subtract $30$ $30$ from both sides
$x$ $x$	$=$ $=$	$150 °$ $150°$

∠ x = 150 °

$/_ x=150°$

Question 3 of 4

Find the value of

x

$x$

$x =$ $x=$ (132)°

Incorrect

Supplementary angles are when two angles have a sum of

180 ° .

$180°.$ Typically, these angles lie on a straight line.

The sum of the interior angles in a triangle is $180 °$ $180°$

To solve for

x

$x$ , find the supplementary angle of

z

$z$

First, we can see from the diagram that the exterior angle

88 °

$88°$ and the interior angle

y

$y$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

y

$y$ .

$y + 88$ $y+88$	$=$ $=$	$180$ $180$
$y + 88$ $y+88$ $- 88$ $-88$	$=$ $=$	$180$ $180$ $- 88$ $-88$	Subtract $88$ $88$ from both sides
$y$ $y$	$=$ $=$	$92 °$ $92°$

Next, since the interior angles of a triangle add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for

z

$z$ .

$y + z + 40$ $y+z+40$	$=$ $=$	$180$ $180$
$92 + z + 40$ $92+z+40$	$=$ $=$	$180$ $180$	Plug in the known values
$z + 132$ $z+132$	$=$ $=$	$180$ $180$	Simplify
$z + 132$ $z+132$ $- 132$ $-132$	$=$ $=$	$180$ $180$ $- 132$ $-132$	Subtract $132$ $132$ from both sides
$z$ $z$	$=$ $=$	$48 °$ $48°$

Finally, we can see from the diagram that the exterior angle

x

$x$ and the interior angle

z

$z$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

x

$x$ .

$x + z$ $x+z$	$=$ $=$	$180$ $180$
$x + 48$ $x+48$	$=$ $=$	$180$ $180$	Plug in the known values
$x + 48$ $x+48$ $- 48$ $-48$	$=$ $=$	$180$ $180$ $- 48$ $-48$	Subtract $48$ $48$ from both sides
$x$ $x$	$=$ $=$	$132 °$ $132°$

∠ x = 132 °

$/_ x=132°$

Question 4 of 4

Find the value of

a

$a$

$a =$ $a=$ (154)°

Incorrect

Supplementary angles are when two angles have a sum of

180 ° .

$180°.$ Typically, these angles lie on a straight line.

The sum of the interior angles in a triangle is $180 °$ $180°$

To solve for

a

$a$ , find the supplementary angle of

z

$z$ .

First, we can see from the diagram that the exterior angle

122 °

$122°$ and the interior angle

x

$x$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

x

$x$ .

$x + 122$ $x+122$	$=$ $=$	$180$ $180$
$x + 122$ $x+122$ $- 122$ $-122$	$=$ $=$	$180$ $180$ $- 122$ $-122$	Subtract $122$ $122$ from both sides
$x$ $x$	$=$ $=$	$58 °$ $58°$

Next, we can see from the diagram that the exterior angle

84 °

$84°$ and the interior angle

y

$y$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

y

$y$ .

$y + 84$ $y+84$	$=$ $=$	$180$ $180$
$y + 84$ $y+84$ $- 84$ $-84$	$=$ $=$	$180$ $180$ $- 84$ $-84$	Subtract $84$ $84$ from both sides
$y$ $y$	$=$ $=$	$96 °$ $96°$

Now, since the interior angles of a triangle add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for

z

$z$ .

$x + y + z$ $x+y+z$	$=$ $=$	$180$ $180$
$58 + 96 + z$ $58+96+z$	$=$ $=$	$180$ $180$	Plug in the known values
$z + 154$ $z+154$	$=$ $=$	$180$ $180$	Simplify
$z + 154$ $z+154$ $- 154$ $-154$	$=$ $=$	$180$ $180$ $- 154$ $-154$	Subtract $154$ $154$ from both sides
$z$ $z$	$=$ $=$	$26 °$ $26°$

Finally, we can see from the diagram that the exterior angle

a

$a$ and the interior angle

z

$z$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

a

$a$ .

$a + z$ $a+z$	$=$ $=$	$180$ $180$
$a + 26$ $a+26$	$=$ $=$	$180$ $180$	Plug in the known values
$a + 26$ $a+26$ $- 26$ $-26$	$=$ $=$	$180$ $180$ $- 26$ $-26$	Subtract $26$ $26$ from both sides
$a$ $a$	$=$ $=$	$154 °$ $154°$

∠ a = 154 °

$/_ a=154°$

Triangle Geometry 3

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