Question

lesson 4 - 2: exit ticket
in the figure shown, what is the value of x?
$x = \square$

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, \((6x + 10)=(x + 17)+(4x-34)\)

Step2: Simplify the right - hand side of the equation

First, simplify \((x + 17)+(4x-34)\):
\((x + 17)+(4x-34)=x+4x+17 - 34=5x-17\)
The equation becomes \(6x + 10=5x-17\)

Step3: Solve for \(x\)

Subtract \(5x\) from both sides of the equation:
\(6x-5x+10=5x-5x - 17\)
\(x+10=-17\)
Subtract \(10\) from both sides:
\(x+10 - 10=-17 - 10\)

Answer:

\(x=-27\)