Question

1. find the value of x

(7x + 4)° (10x − 11)°

Explanation:

Step1: Identify the theorem

The triangle has a midline (since the segments are marked equal), so the angle formed by the midline and the side is equal to the angle at the opposite vertex (by the Midline Theorem and corresponding angle properties, or isosceles triangle properties here as the sides are equal, so the angles related by the midline should be equal? Wait, actually, the two angles given are equal because the line is a midline, so the triangles are similar or the angles are equal. So we set the two angle expressions equal: $7x + 4 = 10x - 11$.

Step2: Solve for x

Subtract $7x$ from both sides: $4 = 3x - 11$.
Add 11 to both sides: $15 = 3x$.
Divide by 3: $x = 5$.

Answer:

$x = 5$