Question

In the figure below, suppose m2<= 30° and m<4=48°.

Complete the statements below.
The sum of the interior angle measures of a triangle must be
So, m<2+m<3+m<4=_?_
We are given that m<2 = 30°
So, m<3 +m<4= _?_°.
From the figure, we can see that m<1 +m<2= _?_°.
Since m<2 = 30°, it must be that m<1=_?_°.
Therefore, m<1 (Choose one A)<
B)=
C) > ) m<3+m<4.

This result is an example of the Exterior Angle Property of Triangles.
For any triangle, the measure of an exterior angle
(Choose one
A) Is less than the sum of the measures of its two remote interior angles.
B) Equals the sum of the measures of its two remote interior angles
C) is greater than the sum of the measures of its two remote interior angles)

Answer 1

Based on the Exterior Angle Property of Triangles, we have been able to prove that m∠1 = m∠3 + m∠4. Thus, option B is the answer.

What is the Exterior Angle Property of Triangles?

The Exterior Angle Property of Triangles states that in a triangle, the measure of an exterior angle is congruent to the sum of the measures of its two remote interior angles.

Thus, we can state the following:

The sum of the interior angle measures of a triangle must be equal to 180 degrees.

So, we would have, m∠2 + m∠3 + m∠4 = 180 degrees.

Given that m∠2 = 30°, so:

m∠3 + m∠4 = 150°

Looking at the figure, m∠1 + m∠2 = 180°.

Since m∠2 = 30°, it must be that m∠1 = 180 - 30 = 150°

Therefore, m∠1 = m∠3 + m∠4 (since m∠3 + m∠4 = 150° and m∠1 = 150°).

This can be said to be as a an example of the Exterior Angle Property of Triangles which states that: the measure of an exterior angle of any triangle option B.