Question

question 8
solve for x.

question 9
solve for x.

Explanation:

Step1: Use the property of isosceles triangle and exterior - angle

In an isosceles triangle (the two sides with the red marks are equal), the base angles are equal. Let the base angles be \(x\). The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, the exterior - angle is \(75^{\circ}\), and the two non - adjacent interior angles are \(x\) (the base angle) and \(x\) (the other base angle).
We know that the exterior - angle formula for a triangle is \(Exterior\ angle=\sum\) of non - adjacent interior angles. So, \(75^{\circ}=x + x\).

Step2: Solve the equation for \(x\)

The equation \(75^{\circ}=2x\). Divide both sides of the equation by 2. We get \(x=\frac{75^{\circ}}{2}\).

Answer:

\(37.5^{\circ}\)