Question

lesson 7
describing the exterior angles o
find the missing angle measures.
132°
d
a
b
m∠cba =

m∠bca =

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, \(2x + 4x=132\).

Step2: Solve the equation for \(x\)

Combine like terms: \(6x = 132\). Then divide both sides by 6: \(x=\frac{132}{6}=22\).

Step3: Find \(m\angle CBA\)

Since \(m\angle CBA = 4x\), substitute \(x = 22\) into the expression. So, \(m\angle CBA=4\times22 = 88^{\circ}\).

Step4: Find \(m\angle BCA\)

Since \(m\angle BCA=2x\), substitute \(x = 22\) into the expression. So, \(m\angle BCA=2\times22 = 44^{\circ}\).

Answer:

\(m\angle CBA = 88^{\circ}\), \(m\angle BCA=44^{\circ}\)