Finding Corresponding Angles: Triangle ABC vs Triangle DEF Comparison

Question

Look at the two triangles below:

Angle B is equal to angle F.

Angle C is equal to angle D.

Which angle corresponds to angle A?

00:00 Which angle corresponds to angle A?

00:03 Corresponding angles according to the given data

00:09 We want to calculate angle A

00:12 The sum of angles in a triangle equals 180

00:17 Therefore, we subtract the known angles from 180 to get angle A

00:27 We'll use the same method to find the expression for angle E

00:36 Let's substitute angles B and C according to the given data

00:50 We see that we got the same expression, therefore they are corresponding angles

01:02 And this is the solution to the question

We use the angle-angle theorem to simulate triangles.

Let's observe the data we already have:

Angles B and F are equal.

Angle C is equal to angle D.

Therefore, the remaining angles must also be equal: angles A and E.

$E$