Question

what is m∠1? 25°, 115°, 65°, 75°

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, for the given triangle, we have the equation $(5x - 10)=40 + 3x$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides: $5x-3x - 10=40+3x-3x$, which simplifies to $2x-10 = 40$. Then add 10 to both sides: $2x-10 + 10=40 + 10$, giving $2x=50$. Divide both sides by 2: $x = 25$.

Step3: Find the measure of $\angle1$

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

Answer:

$115^{\circ}$