Question

Given triangle MNP is isosceles and the two base angles are 6yº and (8y - 16)º. What is the measure of each base angle? (Hint: Sketch and label the triangle first.)

Answer 1

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