Question

the figure is not drawn to scale. 21. if m∠acd = 100 and m∠b = 60, find m∠a.

Explanation:

Step1: Recall exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle ABC\), \(\angle ACD\) is an exterior angle, and \(\angle A\) and \(\angle B\) are the non - adjacent interior angles. So, \(m\angle ACD=m\angle A + m\angle B\).

Step2: Solve for \(m\angle A\)

We can rewrite the formula as \(m\angle A=m\angle ACD - m\angle B\). Given \(m\angle ACD = 100\) and \(m\angle B=60\), then \(m\angle A=100 - 60\).
\(m\angle A = 40\)

Answer:

C. 40