Question

1. determine the value of x in the diagram. enter your answer in the box. x =

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle ABC\), \(\angle ACD\) is an exterior angle. So, \(\angle ACD=\angle B + \angle A\).

Step2: Substitute the known values

We know that \(\angle ACD = 121^{\circ}\) and \(\angle B=36^{\circ}\), and \(\angle A = x^{\circ}\). Then \(121^{\circ}=36^{\circ}+x^{\circ}\).

Step3: Solve for \(x\)

Subtract \(36^{\circ}\) from both sides of the equation: \(x^{\circ}=121^{\circ}- 36^{\circ}\).
\(x = 85\)

Answer:

85