Question

what is the value of a?

( a = square ^ { circ } )

Explanation:

Step1: Apply the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(a + 49^{\circ}=(5a - 39^{\circ})+32^{\circ}\).

Step2: Simplify the right - hand side

Simplify \((5a - 39^{\circ})+32^{\circ}\) to get \(5a-7^{\circ}\). The equation becomes \(a + 49^{\circ}=5a-7^{\circ}\).

Step3: Solve for \(a\)

Subtract \(a\) from both sides: \(49^{\circ}=4a-7^{\circ}\). Then add \(7^{\circ}\) to both sides: \(56^{\circ}=4a\). Divide both sides by \(4\): \(a = 14^{\circ}\).

Answer:

\(14\)