Question

what is ( mangle abc )?
( mangle abc = 15^{circ} )
( mangle abc = 45^{circ} )
( mangle abc = 60^{circ} )
( mangle abc = 75^{circ} )

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. In \(\triangle ABC\), \(\angle ACD\) is an exterior angle. Let \(\angle ABC=x\), \(\angle A = 75^{\circ}\), and \(\angle ACD=135^{\circ}\). Then \(\angle ACD=\angle A+\angle ABC\).

Step2: Solve for \(\angle ABC\)

Substitute the known values into the equation \(135^{\circ}=75^{\circ}+x\).
Subtract \(75^{\circ}\) from both sides: \(x = 135^{\circ}-75^{\circ}\).

$$x=60^{\circ}$$

Answer:

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