Question

what is the value of a?
a + 20^circ
36^circ
4a - 10^circ
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, \(4a - 10=(a + 20)+36\).

Step2: Simplify the equation

First, simplify the right - hand side: \((a + 20)+36=a+56\). Then the equation becomes \(4a-10=a + 56\).

Step3: Solve for \(a\)

Subtract \(a\) from both sides: \(4a-a-10=a - a+56\), which gives \(3a-10 = 56\). Then add \(10\) to both sides: \(3a-10 + 10=56+10\), so \(3a=66\). Divide both sides by \(3\): \(a=\frac{66}{3}\).

Answer:

\(22\)