5. Find the measure of each angle labeled in the diagram, given that line l is

parallel to line m. Use what you know about special angle pairs formed when parallel

lines are cut by a transversal. Also use what you know about vertical angles and linear

pairs.

[tex]5. Find the measure of each angle labeled in the diagram, given that line l is parallel to line m[/tex]

Two angles are equals.

Suppose they are 6y.

Then 6y + 6y + 8y - 16 = 180

20y = 180 +16

20y = 196

y = 9.8

Then one base angle is 6*9.8 = 58.8°

And the other base angle is 8(9.8) - 16 = 62.4.

Now suppose that the two equal angles are 8 y -16

Then 8y -1 6 + 8y - 16 + 6y = 180

Then 16y - 32 = 180

16y = 180 + 32

16y = 212

y = 13.25

One angle is 6(13.25) = 79.5

And the other is 8(13.25) - 16 = 90

This last solution is imposible.

So the answer is 58.8 and 62.4

90 degree

Step-by-step explanation:

Let represent the measure of the third angle. Then, − can represent the measure of the second angle. The

sum of the two angles in the right triangle will be °.

− + =

− =

− + = +

=

=

=

The third angle is and therefore measures °. Replacing with in − gives () − = − = .

Therefore, the measure of the second angle is °. The measure of the third angle is °.