Question

1 from unit 1, lesson 9
use the diagram to find the measure of each angle.
a. ( mangle abc )
b. ( mangle ebd )
c. ( mangle abe )
answer attempt 1 out of 99
a. ( m<abc=square^{circ} )

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. $\angle ABC$ and $\angle EBD$ are vertical angles.

Step2: Find $m\angle ABC$

Since $\angle ABC$ and the $45^{\circ}$ angle are supplementary (they form a linear pair), $m\angle ABC = 180^{\circ}- 45^{\circ}=135^{\circ}$.

Step3: Find $m\angle EBD$

Because $\angle ABC$ and $\angle EBD$ are vertical angles, $m\angle EBD=m\angle ABC = 135^{\circ}$.

Step4: Find $m\angle ABE$

$\angle ABE$ and $\angle ABC$ are supplementary (they form a linear pair), so $m\angle ABE=180^{\circ}-m\angle ABC$. Substitute $m\angle ABC = 135^{\circ}$, then $m\angle ABE = 45^{\circ}$.

Answer:

a. $135^{\circ}$
b. $135^{\circ}$
c. $45^{\circ}$