Question

what is the value of a?
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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, \(a + 50=(a - 18)+(a - 4)\)

Step2: Simplify the right - hand side

Simplify \((a - 18)+(a - 4)\):

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The equation becomes \(a + 50=2a-22\)

Step3: Solve for \(a\)

Subtract \(a\) from both sides of the equation \(a + 50=2a-22\):
\(a+50 - a=2a-22 - a\)
\(50=a - 22\)
Add 22 to both sides: \(50 + 22=a-22 + 22\)

Answer:

\(a = 72\)