Question

1. c 53° d 102° b f

Explanation:

Step1: Find the adjacent angle of \(102^{\circ}\)

The adjacent angle of \(102^{\circ}\) is \(180 - 102=78^{\circ}\) (supplementary angles).

Step2: Use the triangle - angle sum theorem

In \(\triangle BCD\), the sum of interior angles is \(180^{\circ}\). Let \(\angle D=x\). Then \(x + 53+78 = 180\) (triangle - angle sum: \(\angle C+\angle CBD+\angle D = 180^{\circ}\)).

$$x=180-(53 + 78)$$

$$x=180 - 131$$

$$x = 49^{\circ}$$

Answer:

\(49^{\circ}\)