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 °.