Question

6 part a (a) find the value of x in the following figure: part b find the measure of exterior angle ∠acd.

Explanation:

Step1: Use the triangle angle - sum property

In \(\triangle ABC\), the sum of interior angles is \(180^{\circ}\). Let \(\angle A=x^{\circ}\), \(\angle B = 55^{\circ}\), \(\angle ACB=35^{\circ}\). Then \(x + 55+35=180\).

Step2: Solve for \(x\)

Simplify the left - hand side of the equation: \(x+(55 + 35)=x + 90\). So, \(x+90 = 180\). Subtract 90 from both sides: \(x=180 - 90\).

Step3: Use the exterior angle property for \(\angle ACD\)

The exterior angle property of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For \(\triangle ABC\) and exterior angle \(\angle ACD\), \(\angle ACD=\angle A+\angle B\). Since \(x = 90^{\circ}\) (from part A) and \(\angle B=55^{\circ}\), \(\angle ACD=90 + 55\).

Answer:

Part A: \(x = 90\) degrees.
Part B: \(\angle ACD=145^{\circ}\)