Question

in the figure below, triangle abc is an equilateral triangle, and quadrilateral defb is a square. what is m∠abd? a. 45° b. 50° c. 30° d. 20°

Explanation:

Step1: Recall angle - measure of equilateral triangle

In equilateral triangle \(ABC\), each interior angle measures \(60^{\circ}\), so \(\angle ABC = 60^{\circ}\).

Step2: Recall angle - measure of square

In square \(DEFB\), each interior angle measures \(90^{\circ}\), so \(\angle FBD=90^{\circ}\).

Step3: Calculate \(\angle ABD\)

The sum of \(\angle ABC\) and \(\angle ABD\) is \(\angle FBD\). Let \(m\angle ABD = x\). Then \(x + 60^{\circ}=90^{\circ}\), so \(x=90^{\circ}-60^{\circ}=30^{\circ}\).

Answer:

C. \(30^{\circ}\)