Question

Lamar wanted to explain why the measure of angle 5 is equal to the sum of the measures of angles 1 and 3. Which geometry concepts should be used in Lamar’s work?
A. supplementary angles and the sum of the measures of interior angles of a triangle
B. complementary angles and the sum of the measures of interior angles of a triangle
C. supplementary angles and vertical angles
D. the sum of the measures of interior angles of a triangle and vertical angles

Answer 1

Answer: option A

Step-by-step explanation:

Because supplementary angles and the sum of the measure of interior angles of a triangle

Answer 2

In this question, angle 5 and angle 2 are linear pair. And angles of linear pair are supplementary angles .

Therefore

$\angle 5 + \angle 2=180$

And sum of interior angles of a triangle is 180 degree, that is

$\angle 1 + \angle 2 + \angle 3 =180$

SInce both the equations have 180 in the right side, left side of both equations are equal too . That is

$\angle 5 + \angle 2 = \angle 1 + \angle 2 + \angle 3$

Which gives

$\angle 5=\angle 1 + \angle 3$

So the correct option is A .