Question

practice d: (first taught in lesson 31) find a. after you enter your answer press go. 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, \(6y=2y + 84\).
Solve for \(y\):
\(6y-2y=84\)
\(4y = 84\)
\(y=\frac{84}{4}=21\)

Step2: Use the angle - sum property of a linear pair

Since \(a\) and \(6y\) form a linear pair (\(a + 6y=180\)), substitute \(y = 21\) into the equation.
\(a+6\times21=180\)
\(a + 126=180\)
\(a=180 - 126\)

Answer:

\(a = 54\)