Question

what is the measure of the unknown angle? question 10(multiple choice worth 5 points) (14.03 lc) a 72° angle is decomposed into two angles, one of which is 59°. what is the measure of the unknown angle?

Explanation:

Step1: Recall angle - addition property

The two angles on a straight - line sum to 180°. Let the unknown angle be \(n\). We have \(n + 58^{\circ}=180^{\circ}\).

Step2: Solve for \(n\)

Subtract 58° from both sides of the equation: \(n=180^{\circ}-58^{\circ}\).
\(n = 122^{\circ}\)

for second question:

Step1: Use angle - decomposition property

If a 72° angle is decomposed into two angles, and one angle is 59°, let the unknown angle be \(x\). Then \(72^{\circ}=x + 59^{\circ}\).

Step2: Solve for \(x\)

Subtract 59° from both sides of the equation: \(x=72^{\circ}-59^{\circ}\).
\(x = 13^{\circ}\)

Answer:

D. 122°