Question

1. consider the diagram.

a. describe the relationship among $\angle dac$, $\angle cae$, and $\angle eab$.
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 $\angle eab$?

Explanation:

Part a

From the diagram, $\angle DAC = \angle CAE = \angle EAB = x^\circ$ (marked equal). Together, they form $\angle DAB$, which is a right angle ($90^\circ$), so $\angle DAC + \angle CAE + \angle EAB = \angle DAB = 90^\circ$.

Part b

Step1: Set up the equation

Since $\angle DAC + \angle CAE + \angle EAB = 90^\circ$ and each angle is $x^\circ$, we have $x + x + x = 90$.

Step2: Solve the equation

Simplify the left - hand side: $3x = 90$. Divide both sides by 3: $x=\frac{90}{3}=30$.

Part c

Step1: Substitute $x = 30$ into the left - hand side of the equation

Substitute $x = 30$ into $3x$. We get $3\times30 = 90$.

Step2: Compare with the right - hand side

The right - hand side of the equation $x + x + x=90$ is $90$. Since $3\times30 = 90$, the left - hand side equals the right - hand side when $x = 30$, so the solution is correct.

Part d

Answer:

$\angle DAC$, $\angle CAE$, and $\angle EAB$ are congruent (each measures $x^\circ$) and their sum equals $\angle DAB$ (a right angle, $90^\circ$).