S is in the interior of ∠PQR, m∠PQS = 87°, and m∠SQR = 33°. Find m∠PQR.
To find the measure of ∠PQR, we can use the angle sum property of triangles. In a triangle, the sum of the measures of its angles is always 180 degrees.
Given that S is in the interior of ∠PQR, it means that the angle ∠PQS and ∠SQR form a linear pair with ∠PQR. A linear pair of angles is formed when two angles are adjacent angles and their non-common sides form a straight line.
Now, we know that m∠PQS is 87 degrees and m∠SQR is 33 degrees. We can find the measure of ∠PQR by subtracting the sum of these two angles from 180 degrees since the three angles in triangle PQR add up to 180 degrees.
Using the angle sum property,
m∠PQR = 180° - (m∠PQS + m∠SQR)
m∠PQR = 180° - (87° + 33°)
m∠PQR = 180° - 120°
m∠PQR = 60°
Therefore, the measure of ∠PQR is 60 degrees.
To find the measure of ∠PQR, we can first use the fact that the angles in a triangle add up to 180°.
Step 1: Start with the fact that the sum of the measures of ∠PQS and ∠SQR is equal to the measure of ∠PQR.
∠PQS + ∠SQR = ∠PQR
Step 2: Substitute the given angle measures into the equation.
87° + 33° = ∠PQR
Step 3: Simplify the equation.
120° = ∠PQR
Therefore, m∠PQR is 120°.
Draw a diagram. Clearly
m∠PQR = m∠PQS + m∠SQR