Question

1. in △abc, the measure of the exterior angle at b is 100. if m∠a is 4 times larger than m∠c, find m∠c.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. So, \(m\angle A+m\angle C = 100\).

Step2: Set up an equation based on the relationship between \(\angle A\) and \(\angle C\)

Let \(m\angle C=x\). Since \(m\angle A\) is \(4\) times larger than \(m\angle C\), then \(m\angle A = 4x\).

Step3: Solve the equation

Substitute \(m\angle A = 4x\) and \(m\angle C=x\) into \(m\angle A+m\angle C = 100\). We get \(4x + x=100\), which simplifies to \(5x=100\).
Divide both sides by \(5\): \(x=\frac{100}{5}=20\).

Answer:

\(m\angle C = 20\)