Question

1. determine the measure of the angle.

a) m∠a=
b) m∠c=
c) m∠c=
d) m∠a=

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Solve for a)

Given two angles of a triangle are 99° and 41°. Let \(m\angle A\) be the third - angle. Then \(m\angle A=180-(99 + 41)=180 - 140=40^{\circ}\)

Step3: Solve for b)

Given two angles of a triangle are 60° and 65°. Let \(m\angle C\) be the third - angle. Then \(m\angle C=180-(60 + 65)=180 - 125 = 55^{\circ}\)

Step4: Solve for c)

Given a right - triangle with one non - right angle 48°. Let \(m\angle C\) be the third - angle. Since one angle is 90°, then \(m\angle C=180-(90 + 48)=180 - 138 = 42^{\circ}\)

Step5: Solve for d)

Given two angles of a triangle are 110° and 34°. Let \(m\angle A\) be the third - angle. Then \(m\angle A=180-(110 + 34)=180 - 144 = 36^{\circ}\)

Answer:

a) \(m\angle A = 40^{\circ}\)
b) \(m\angle C = 55^{\circ}\)
c) \(m\angle C = 42^{\circ}\)
d) \(m\angle A = 36^{\circ}\)