Question

problem 22: (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 an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(5x=2x + 57\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides of the equation \(5x=2x + 57\).
\(5x-2x=2x + 57-2x\)
\(3x=57\)
Divide both sides by 3: \(x = 19\).

Step3: Use the linear - pair relationship

Since \(5x\) and \(a\) form a linear pair (they are adjacent angles on a straight line), \(5x+a = 180\).
Substitute \(x = 19\) into \(5x\): \(5x=5\times19 = 95\).
Then, \(a=180 - 5x\).
\(a=180-95\).

Answer:

\(85\)