Question

∠3 and ∠4 are supplementary angles. given the measure of ∠3, find m∠4. 17. m∠3 = 75° 18. m∠3 = 116°

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle3 + m\angle4=180^{\circ}\), then \(m\angle4 = 180^{\circ}-m\angle3\).

Step2: Solve for \(m\angle4\) in problem 17

Given \(m\angle3 = 75^{\circ}\), then \(m\angle4=180^{\circ}-75^{\circ}=105^{\circ}\).

Step3: Solve for \(m\angle4\) in problem 18

Given \(m\angle3 = 116^{\circ}\), then \(m\angle4=180^{\circ}-116^{\circ}=64^{\circ}\).

Answer:

1. \(105^{\circ}\)
2. \(64^{\circ}\)