Question

in the diagram, ∠bad is a straight angle. use this diagram for problems 1–4.

1. describe the relationship between ∠bac and ∠cad.
2. write an equation for the angle relationship and solve for x.
3. check your solution to the equation.
4. what is the measure of ∠bac?

Explanation:

Problem 1

Since $\angle BAD$ is a straight angle (measures $180^\circ$), and $\angle BAC$ and $\angle CAD$ are adjacent angles that together make up $\angle BAD$, they are supplementary (sum to $180^\circ$) and form a linear pair.

Problem 2

Step1: Identify the angle relationship

$\angle BAC + \angle CAD = \angle BAD$. Since $\angle BAD$ is a straight angle, $\angle BAD = 180^\circ$. So, $x + 132 = 180$.

Step2: Solve for $x$

Subtract $132$ from both sides of the equation: $x = 180 - 132$. Calculate $180 - 132 = 48$. So, $x = 48$.

Problem 3

Step1: Substitute $x = 48$ into the equation

Left - hand side: $48+132$.

Step2: Calculate the sum

$48 + 132=180$, which is equal to the measure of a straight angle ($\angle BAD$). So the solution $x = 48$ satisfies the equation $x + 132 = 180$.

Problem 4

Answer:

$\angle BAC$ and $\angle CAD$ are supplementary angles (they form a linear pair, so their sum is $180^\circ$).