Question

find the value of a.

1. a°=?

45°
73°
107°
253°

Explanation:

Step1: Use the exterior angle property of a triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let's first find the non - exterior angle adjacent to \(a\).
The non - exterior angle adjacent to \(a\) (let's call it \(x\)) can be found using the fact that the sum of angles in a triangle is \(180^{\circ}\). But we can also use the exterior angle property for a straight line.

We know that the sum of angles on a straight line is \(180^{\circ}\). Also, by the exterior angle property of a triangle (an exterior angle of a triangle is equal to the sum of the two opposite interior angles), the non - exterior angle adjacent to \(a\) (let's call it \(y\)): \(y=51^{\circ}+56^{\circ}\) (sum of two non - adjacent interior angles of the triangle).
\(y = 51+56=107^{\circ}\)

Step2: Use the linear pair property

Since \(a\) and \(y\) form a linear pair (angles on a straight line), and for a linear pair \(a + y=180^{\circ}\)
Substitute \(y = 107^{\circ}\) into the equation \(a + y=180^{\circ}\)
\(a=180 - y\)
\(a=180- 107\)
\(a = 73^{\circ}\)

Answer:

\(73^{\circ}\)