Question

1. in the diagram, ∠cab is a straight angle,

a. describe the relationship between ∠cad and ∠dab.
b. write an equation for the angle relationship and solve for x.
c. check your solution to the equation.
d. what is the measure of ∠dab?

Explanation:

Part a

Step1: Identify angle relationship

Since \( \angle CAB \) is a straight angle (\( 180^\circ \)), \( \angle CAD \) and \( \angle DAB \) are adjacent angles that form a linear pair. A linear pair of angles is supplementary, meaning their sum is \( 180^\circ \). Also, \( \angle CAD = 24^\circ \), so \( \angle CAD \) and \( \angle DAB \) are supplementary angles.

Step1: Set up the equation

As \( \angle CAD + \angle DAB = 180^\circ \) (linear pair), and \( \angle CAD = 24^\circ \), \( \angle DAB = x^\circ \), the equation is \( 24 + x = 180 \).

Step2: Solve for \( x \)

Subtract \( 24 \) from both sides: \( x = 180 - 24 = 156 \).

Step1: Substitute \( x = 156 \)

Substitute \( x = 156 \) into the left - hand side of the equation \( 24 + x \): \( 24+156 = 180 \).

Step2: Compare with right - hand side

The right - hand side of the equation \( 24 + x = 180 \) is \( 180 \). Since \( 24 + 156=180 \), the solution \( x = 156 \) satisfies the equation.

Answer:

\( \angle CAD \) and \( \angle DAB \) are supplementary (form a linear pair, sum to \( 180^\circ \)).

Part b