Question

c.) find: m∠1
40°
30°
1
d.) find: m∠2
70°
113°
2

Explanation:

Step1: Use the exterior angle theorem for part c

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the first triangle, \(\angle1\) is an exterior angle. So, \(m\angle1=30^{\circ}+40^{\circ}\)

Step2: Calculate \(m\angle1\)

\(m\angle1 = 70^{\circ}\)

Step3: Use the exterior angle theorem for part d

Let the non - given interior angle adjacent to the \(113^{\circ}\) exterior angle be \(x\). We know that \(x = 180^{\circ}-113^{\circ}=67^{\circ}\) (linear pair). Then, using the triangle angle sum theorem (\(m\angle2+70^{\circ}+x = 180^{\circ}\)), substitute \(x = 67^{\circ}\)
\(m\angle2=180^{\circ}-70^{\circ}-67^{\circ}\)

Step4: Calculate \(m\angle2\)

\(m\angle2 = 43^{\circ}\)

Answer:

c. \(70^{\circ}\)
d. \(43^{\circ}\)