Question

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

Explanation:

Step1: Find the exterior angle at C

The angle adjacent to \(135^\circ\) on the straight line is \(180^\circ - 135^\circ = 45^\circ\) (since they are supplementary).

Step2: Use the triangle angle - sum property

In \(\triangle ABC\), we know one angle at \(A\) is \(75^\circ\), the angle at \(C\) (interior) is \(45^\circ\). Let \(\angle ABC=x\). We know that the sum of angles in a triangle is \(180^\circ\), so \(75^\circ + 45^\circ+x=180^\circ\).

Step3: Solve for \(x\)

First, calculate \(75^\circ+ 45^\circ=120^\circ\). Then, \(x = 180^\circ- 120^\circ = 60^\circ\).

Answer:

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