Question

what is the value of a?
a + 47°
a + 17°
a - 34°
a = □°

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(a + 47^{\circ}=(a + 17^{\circ})+(a-34^{\circ})\)

Step2: Simplify the right - hand side of the equation

First, simplify \((a + 17^{\circ})+(a-34^{\circ})\):
\((a + 17^{\circ})+(a-34^{\circ})=a + 17^{\circ}+a-34^{\circ}=2a-17^{\circ}\)
The equation becomes \(a + 47^{\circ}=2a-17^{\circ}\)

Step3: Solve for \(a\)

Subtract \(a\) from both sides of the equation:
\(a - a+47^{\circ}=2a - a-17^{\circ}\)
\(47^{\circ}=a-17^{\circ}\)
Then add \(17^{\circ}\) to both sides:
\(a=47^{\circ}+17^{\circ}\)

Answer:

\(64\)