Question

Please tell me the answer.

Answer 1

Answer:

-The measure of $\angle A$ :

$\angle A = 144\textdegree$

-The measure of $\angle B$ (if needed):

$\angle B = 144\textdegree$

Step-by-step explanation:

-Set the measure of $\angle A$ on one side and set the measure of $\angle B$ on the other side and it will be written as:

$10x + 24 = 6x + 72$

-Then, solve for $x$ :

$10x + 24 = 6x + 72$

$10x + 24 - 6x = 6x - 6x + 72$

$4x + 24 = 72$

$4x + 24 - 24 = 72 - 24$

$4x = 48$

$\frac{4x}{4} = \frac{48}{4}$

$x = 12$

-After you have found the value of $x$, plug in both the measure of $\angle A$ and $\angle B$ in order to get the actual angle measurement of $\angle A$ and $\angle B$ :

Finding the measure of $\angle A$ :

$\angle A = 10(12) + 24$

$\angle A = 120 + 24$

$\angle A = 144\textdegree$

Finding the measure of $\angle B$ :

$\angle B = 6(12) + 72$

$\angle B = 72 + 72$

$\angle B = 144\textdegree$

-Notice: That reason why both $\angle A$ and $\angle B$ have the same measurements, its because they are Alternate Exterior Angles, based on the diagram shown.