Question

part b: complementary/supplementary

1. ∠p and ∠q are complementary. if m∠p = 37°, find m∠q
2. ∠r and ∠s are supplementary. if m∠r = 108°, find m∠s
3. in diagram 2, vertical angles are equal. if one angle is 50°, find x = ___°

Explanation:

Problem 5:

Step1: Recall complementary angles

Complementary angles sum to \(90^\circ\). Let \(m\angle Q = x\). Then \(m\angle P + m\angle Q = 90^\circ\).

Step2: Substitute \(m\angle P = 37^\circ\)

\(37^\circ + x = 90^\circ\). Solve for \(x\): \(x = 90^\circ - 37^\circ = 53^\circ\).

Step1: Recall supplementary angles

Supplementary angles sum to \(180^\circ\). Let \(m\angle S = y\). Then \(m\angle R + m\angle S = 180^\circ\).

Step2: Substitute \(m\angle R = 108^\circ\)

\(108^\circ + y = 180^\circ\). Solve for \(y\): \(y = 180^\circ - 108^\circ = 72^\circ\).

Step1: Recall vertical angles property

Vertical angles are equal. If one angle is \(50^\circ\), its vertical angle (which is \(x^\circ\) here) is also \(50^\circ\) (assuming the \(50^\circ\) angle and \(x^\circ\) are vertical angles from the diagram context).

Answer:

\(53^\circ\)

Problem 6: