Question

1. consider the diagram.

a. describe the relationship between $\angle cab$ and $\angle dab$.
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 $\angle cab$?

Explanation:

Part a

From the diagram, $\angle CAD$ is a right angle ($90^\circ$), so $\angle CAB + \angle DAB = 90^\circ$, meaning they are complementary.

Part b

Step1: Identify angle relationship

$\angle CAB + \angle DAB = 90^\circ$ (complementary angles, as $\angle CAD = 90^\circ$).

Step2: Write the equation

Given $\angle DAB = 56^\circ$ and $\angle CAB = x^\circ$, the equation is $x + 56 = 90$.

Step3: Solve for $x$

Subtract $56$ from both sides: $x = 90 - 56 = 34$.

Part c

Step1: Substitute $x = 34$ into the equation

Left - hand side: $34+56 = 90$.

Step2: Compare with right - hand side

The right - hand side of the equation $x + 56=90$ is $90$. Since $34 + 56=90$, the solution $x = 34$ satisfies the equation.

Part d

Answer:

$\angle CAB$ and $\angle DAB$ are complementary angles (their sum is $90^\circ$).