Question

what is ( mangle abc )?
options: ( mangle abc = 60^circ ), ( mangle abc = 75^circ ), ( mangle abc = 45^circ ), ( mangle abc = 15^circ )
(there is a diagram with triangle ( abc ), angle at ( a ) is ( 75^circ ), angle adjacent to ( c ) on the straight line is ( 135^circ ), and points ( b, d ) on a straight line)

Explanation:

Step1: Find the interior angle at C

The angle adjacent to \(135^\circ\) on the straight line is \(180^\circ - 135^\circ = 45^\circ\) (linear pair).

Step2: Use triangle angle sum

In \(\triangle ABC\), the sum of angles is \(180^\circ\). Given \(\angle A = 75^\circ\) and \(\angle ACB = 45^\circ\), then \(\angle ABC = 180^\circ - 75^\circ - 45^\circ = 60^\circ\).

Answer:

\(m\angle ABC = 60^\circ\) (the option with \(m\angle ABC = 60^\circ\))