Answer:
15. A
16. B
Step-by-step explanation:
15. x=15
The sum of the measurements of the angles of a triangle is 180°, and only one interior angle is given, so we have to find the other two interior angles. Exterior and interior angles are supplementary to each other, so their total sum is 180°, and since there are two given exterior, we have to find their values and solve for x in order for us to find the measurements of the other two interior angles. Let x=15
Substitute:
5x+6
5(15)+6
75+6
=81°, this is the first exterior angle, so the adjacent angle to it, is 99° since the two are supplementary angles.
8x+23
8(15)+23
120+23
=143°, this is the second exterior angle, and the angle adjacent to it is 37° since they are supplementary to each other.
Now, we all have the three measurement of the angles of the triangle.
44°+99°+37°=180°
the total of the three interior angles is 180°, which satisfies the definition of a triangle
16.
8x+23
8(15)+23
120+23
=143°
