Question

2
write the equation for the exterior angle theorem:
solve for x: x=
the measurement of the exterior angle equals

Explanation:

Step1: Apply 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 the equation is \(2x - 2=x + 45\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation:
\(2x-x-2=x - x+45\)
\(x-2 = 45\)
Add 2 to both sides:
\(x-2 + 2=45 + 2\)
\(x = 47\)

Step3: Find the measure of the exterior angle

Substitute \(x = 47\) into \(2x-2\)
\(2x-2=2\times47-2\)
\(=94 - 2\)
\(=92\)

Answer:

Equation: \(2x - 2=x + 45\)
\(x = 47\)
Exterior angle measurement: \(92^{\circ}\)