Question

what is the value of a?

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $a + 49^{\circ}=(a - 15^{\circ})+(a + 15^{\circ})$.

Step2: Simplify the right - hand side

$(a - 15^{\circ})+(a + 15^{\circ})=a - 15^{\circ}+a + 15^{\circ}=2a$.

Step3: Solve for a

We have the equation $a + 49^{\circ}=2a$. Subtract $a$ from both sides: $49^{\circ}=2a - a$. So, $a = 49^{\circ}$.

Answer:

$49$