Question

a figure with parallel lines m and n is shown what are the measures of angles A, B, and C?

Answer 1

Let me draw onto the given figure to better understand the problem.

Please refer to the figure below.

As you can see from the figure, angle A is equal to angle 53°.

They are called "Alternate Interior Angles" and they are always equal.

Similarly, angles 37° drawn in red color are also "Alternate Interior Angles".

Now we can find angle B.

$53\degree+\angle B+37\degree=180\degree$

Angle B, angle 53°, and angle 37° form a "straight-line angle" that is 180°.

$\begin{gathered} 53\degree+\angle B+37\degree=180\degree \\ 53\degree+37\degree\angle B=180\degree \\ 90\degree+\angle B=180\degree \\ \angle B=180\degree-90\degree \\ \angle B=90\degree \end{gathered}$

So the angle B is 90°

Now angle C and the sum of angle 53 and angle B are equal.

They are called "Vertically opposite angles" and they are always equal.

So we can write,

$\begin{gathered} \angle C=\angle B+53\degree \\ \angle C=90+53\degree \\ \angle C=143\degree \end{gathered}$

Therefore, the angles A, B, and C are

$\begin{gathered} \angle A=53\degree \\ \angle B=90\degree \\ \angle C=143\degree \end{gathered}$