Question

question 16
∠1 and ∠2 are supplementary angles. what are the measures of the two angles?
(a) ∠1 = 9°, ∠2 = 81°
(b) ∠1 = 18°, ∠2 = 162°
(c) ∠1 = 20°, ∠2 = 162°
(d) ∠1 = 10°, ∠2 = 81°

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(x + 9x=180\).

Step2: Solve the equation

Combine like - terms: \(10x = 180\). Then, divide both sides by 10: \(x=\frac{180}{10}=18\).

Step3: Find the measures of the angles

\(\angle1=x = 18^{\circ}\), \(\angle2 = 9x=9\times18 = 162^{\circ}\).

Answer:

B. \(\angle1 = 18^{\circ},\angle2 = 162^{\circ}\)