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Using Bearings and Distances to Find AnglesUsing Bearings and Distances to Find Angles
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Question 1 of 2
1. Question
Find the value of `angle PQR` using the bearing of `Q` from `P`.
- `/_PQR=` (146)`°`
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First, we can add a vertical line that goes through point `Q`.
add a vertical line through point QThis will indicate that part of `angle PQR` is a right angle, which is `90°`.
Next, notice that the two vertical lines are parallel.From there, we can see that a part of `angle PQR` is an alternate angle to `angle NPQ`.
Since alternate angles are equal, the missing angle also measures `• 56°`.Finally, we can add `• 56°` to the right angle to find the value of `angle PQR`.`/_PQR` `=` `90°+56°` `=` `146°` `/_ PQR=146°` -
Question 2 of 2
2. Question
Find the value of interior angles `X`, `Y`, and `Z` using the given bearings.
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`angleX=` (49)`°``angleY=` (40)`°``angleZ=` (91)`°`
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Complementary angles are when two angles have a sum of `90°.` Typically, these angles form a right angle.The sum of the interior angles in a triangle is `180°`.First, notice that `angleX` and the given bearing of `B` from `A` are complementary angles.
Since complementary angles are equal to `90°`, we can simply subtract the bearing of `B` from `A` to find the measure of `angleX``angleX` `=` `90°-41°` `=` `49°` Next, notice that `angleY` and the given bearing of `B` from `C` complementary angles.
Since complementary angles are equal to `90°`, we can simply subtract the bearing of `B` from `C` to find the measure of `angleY``angleY` `=` `90°-50°` `=` `40°` Finally, to find the measure of `angleZ`, subtract the sum of `angleX` and `angleY` from `180°`, which is the sum of the interior angles of a triangle.`angleZ` `=` `180°-(49°+40°)` `=` `180°-89°` `=` `91°` `angleX=49°``angleY=40°``angleZ=91°` -
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