Question

what is the value of a? a =

Explanation:

Step1: Apply 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, \(7a + 20=(a + 45)+(3a + 29)\)

Step2: Simplify the right - hand side of the equation

First, simplify \((a + 45)+(3a + 29)\):
\((a+3a)+(45 + 29)=4a+74\)
The equation becomes \(7a + 20=4a+74\)

Step3: Solve for \(a\)

Subtract \(4a\) from both sides:
\(7a-4a + 20=4a-4a+74\)
\(3a+20 = 74\)
Subtract \(20\) from both sides:
\(3a+20-20=74 - 20\)
\(3a=54\)
Divide both sides by \(3\):
\(a=\frac{54}{3}\)

Answer:

\(18\)