Question

find the measure of ∠1.

Explanation:

Step1: Apply 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, \(5x - 10=40 + 3x\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(5x-3x - 10=40+3x - 3x\), which simplifies to \(2x-10 = 40\).
Add \(10\) to both sides: \(2x-10 + 10=40 + 10\), so \(2x=50\).
Divide both sides by \(2\): \(x=\frac{50}{2}=25\).

Step3: Find the measure of \(\angle1\)

Substitute \(x = 25\) into the expression for \(\angle1\) (\(5x-10\)).
\(\angle1=5\times25-10=125 - 10=115^{\circ}\).

Answer:

\(115^{\circ}\)