Question

In the diagram of ABC, BC is extended to D, m

Answer 1

Answer:

The measure of angle A is;

$m\angle A=20^{\circ}$

Explanation:

Given the triangle in the attached image;

$m\angle ACB+m\angle ACD=180^{\circ}$

sum of angles on a straight line;

$\begin{gathered} m\angle ACB+m\angle ACD=180^{\circ} \\ 6y+3y=180 \\ 9y=180 \\ y=\frac{180}{9} \\ y=20 \end{gathered}$

Also;

$\begin{gathered} m\angle ACD=m\angle ABC+m\angle A \\ 3y=2y+m\angle A \\ m\angle A=3y-2y \\ m\angle A=y=20 \\ m\angle A=20^{\circ} \end{gathered}$

Therefore, the measure of angle A is;

$m\angle A=20^{\circ}$