Question

Which of the following statements must be true about this diagrarn? Check allthat applyA. The degree measure of 24 equals the sum of the degreemeasures of 21 and 22.B. The degree measure of 24 equals the sum of the degreemeasures of 22 and 23.C. The degree measure of 23 equals the sum of the degreemeasures of 21 and 22D. m24 is greater than m22,O E m23 is greater than m22Em24 is greater than m21

Answer 1

In the given triangle we have the following:

A. The sum of the inner angles of a triangle is always equal to 180, that is:

$\angle1+\angle2+\angle3=180$

From this, we can solve for the sum of angles 1 and 2 and we get:

$\angle1+\angle2=180-\angle3$

Now, we also know that angles 3 and 4 are supplementary angles and therefore their sum is 180 degrees, that is:

$\angle4+\angle3=180$

Solving for angle 4:

$\angle4=180-\angle3$

Equating both results we get:

$\angle1+\angle2=\angle4$

Therefore, it is true that angle 4 is the sum of angles 1 and 2.

B. We have that the sum of angles 2 and 3 is:

$\angle2+\angle3=180-\angle1$

If this were equal to angle 4 we would have:

$\begin{gathered} \angle4=180-\angle1 \\ \angle4+\angle1=180 \end{gathered}$

B