Triangle Geometry 3

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Geometry

Angles

Triangle Geometry

Triangle Geometry 3

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Question 1 of 4

1. Question
Find the value of $a$
- $a=$ (40)°
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Supplementary angles are when two angles have a sum of $180°.$ 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 $180°$

To solve for $a$ , find the measure of the missing interior angles, add it to $a$ and set their sum to $180°$ .

First, we can see from the diagram that the exterior angle $110°$ and the interior angle $b$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to $180°,$ add the angle measures and set their sum to $180°.$ Then, solve for the value of $a$ .

$b+110$ $=$ $180$

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

$b$ $=$ $70°$

Next, since the base angles in an isosceles triangle are equal, $c$ is equal to $70˚$

$c$ $=$ $70$

Finally, since the interior angles of a triangle add to $180°,$ add the angle measures and set their sum to $180°.$ Then, solve for $b$ .

$a+b+c$ $=$ $180$

$a+70+70$ $=$ $180$ Plug in the known values

$a+140$ $=$ $180$ Simplify

$a+140$ $-140$ $=$ $180$ $-140$ Subtract $140$ from both sides

$a$ $=$ $40°$

$/_ a=40°$

Question 2 of 4

Find the value of

$x$

$x=$ (150)°

Question 3 of 4

Find the value of

$x$

$x=$ (132)°

Question 4 of 4

4. Question
Find the value of $a$
- $a=$ (154)°
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Supplementary angles are when two angles have a sum of $180°.$ Typically, these angles lie on a straight line.

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

To solve for $a$ , find the supplementary angle of $z$ .

First, we can see from the diagram that the exterior angle $122°$ and the interior angle $x$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to $180°,$ add the angle measures and set their sum to $180°.$ Then, solve for the value of $x$ .

$x+122$ $=$ $180$

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

$x$ $=$ $58°$

Next, we can see from the diagram that the exterior angle $84°$ and the interior angle $y$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to $180°,$ add the angle measures and set their sum to $180°.$ Then, solve for the value of $y$ .

$y+84$ $=$ $180$

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

$y$ $=$ $96°$

Now, since the interior angles of a triangle add to $180°,$ add the angle measures and set their sum to $180°.$ Then, solve for $z$ .

$x+y+z$ $=$ $180$

$58+96+z$ $=$ $180$ Plug in the known values

$z+154$ $=$ $180$ Simplify

$z+154$ $-154$ $=$ $180$ $-154$ Subtract $154$ from both sides

$z$ $=$ $26°$

Finally, we can see from the diagram that the exterior angle $a$ and the interior angle $z$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to $180°,$ add the angle measures and set their sum to $180°.$ Then, solve for the value of $a$ .

$a+z$ $=$ $180$

$a+26$ $=$ $180$ Plug in the known values

$a+26$ $-26$ $=$ $180$ $-26$ Subtract $26$ from both sides

$a$ $=$ $154°$

$/_ a=154°$

Triangle Geometry 3

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

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

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

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

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

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

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

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

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

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

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

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