Question

Which of the following statements must be true about this diagram? check all that apply

Answer 1

B. m<4 is greater than m<2

C. m<4 is greater than m<1

F. The degree measure of <4 equals the sum of the degree measures of <1 and <2

Answer 2

B. m∠4 is greater than m∠2

C. m∠4 is greater than m∠1

F. The degree measure of m∠4 equals the sum of the degree measures of m∠1 and m∠2

Explanation:

From the given triangle. ∠1. ∠2, ∠3 are the interior angles of the triangle.

∠4 is the extended angle of ∠3. Which is called an exterior angle.

Here we have to use the statement of exterior angle of a triangle.

An exterior angle of a triangle is the sum of the opposite interior angles.

Therefore, m∠4 = m∠1 + m∠2

So, the following options are true:

B. m∠4 is greater than m∠2 {by the exterior angle theorem]

C. m∠4 is greater than m∠1 {by the exterior angle theorem]

F. The degree measure of m∠4 equals the sum of the degree measures of m∠1 and m∠2 {by the exterior angle theorem]