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.)

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

 

2(10 - 13x) + 9x = -34x + 6020 - 26x + 9x = -34x + distributive property-17x = -34x + subtraction property (subtracted 20 from both sides)17x = addition property (added 34x to both sides)x = 40/ division property (divided both sides by 17)