Question

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

Answer 1

The measure of angle A is;

`m\angle A=20^(\circ)`

Step-by-step 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=(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)`