Question

1. in the accompanying diagram, ∠acd is an exterior angle of △abc. if m∠b = 40, m∠a = 2x, and m∠acd = 3x. what is the value of x?

Explanation:

Step1: Use the exterior angle theorem

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

Step2: Substitute the given values

Substitute \(m\angle B = 40\), \(m\angle A=2x\), and \(m\angle ACD = 3x\) into the equation: \(3x=2x + 40\).

Step3: Solve for \(x\)

Subtract \(2x\) from both sides of the equation: \(3x-2x=2x + 40-2x\).

Answer:

\(x = 40\)