Question

what is m∠abc?
o m∠abc = 15°
o m∠abc = 45°
o m∠abc = 60°
o m∠abc = 75°

Explanation:

Step1: Recall 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, \(\angle ACD=\angle BAC+\angle ABC\).

Step2: Substitute known values

We know that \(\angle ACD = 135^{\circ}\) and \(\angle BAC=75^{\circ}\). Let \(\angle ABC = x\). Then \(135^{\circ}=75^{\circ}+x\).

Step3: Solve for \(x\)

Subtract \(75^{\circ}\) from both sides of the equation: \(x=\angle ABC=135^{\circ}-75^{\circ}=60^{\circ}\).

Answer:

\(m\angle ABC = 60^{\circ}\)