Question

name: avalynn
complementary, supplementary, vertical angles
identify if the pairs of angles are supplementary, complementary, or vertical.
calculate the measurements of the angles.

1. ∠dab and ∠eac are ______ angles.
2. ∠dab measures ______ °.
3. ∠eac and ∠bac are ______ angles.
4. ∠bac measures ______ °.
5. ∠bac and ∠dae are ______ angles.
6. ∠dae measures ______ °.

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. $\angle DAB$ and $\angle EAC$ are vertical angles, so $\angle DAB = \angle EAC = 43^\circ$.

Step2: Find supplementary pair sum

Supplementary angles sum to $180^\circ$. $\angle EAC + \angle BAC = 180^\circ$.

Step3: Calculate $\angle BAC$

Substitute $\angle EAC=43^\circ$:
$\angle BAC = 180^\circ - 43^\circ = 137^\circ$

Step4: Identify $\angle BAC$ vertical angle

$\angle BAC$ and $\angle DAE$ are vertical angles, so $\angle DAE = \angle BAC = 137^\circ$.

Answer:

$\angle DAB$ and $\angle EAC$ are vertical angles.
$\angle DAB$ measures $\boldsymbol{43}$ °.
$\angle EAC$ and $\angle BAC$ are supplementary angles.
$\angle BAC$ measures $\boldsymbol{137}$ °.
$\angle BAC$ and $\angle DAE$ are vertical angles.
$\angle DAE$ measures $\boldsymbol{137}$ °.