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Question 1 of 2
Find the value of ∠PQR using the bearing of Q from P.
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First, we can add a vertical line that goes through point Q.
add a vertical line through point Q
This will indicate that part of ∠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 ∠PQR is an alternate angle to ∠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 ∠PQR.
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Question 2 of 2
Find the value of interior angles X, Y, and Z using the given bearings.
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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 ∠X 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 ∠X
Next, notice that ∠Y 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 ∠Y
Finally, to find the measure of ∠Z, subtract the sum of ∠X and ∠Y from 180°, which is the sum of the interior angles of a triangle.
| ∠Z |
= |
180°-(49°+40°) |
|
= |
180°-89° |
|
= |
91° |
