my name is Amanda

high school question

In triangle ABC; the measure of angle A is 20 degrees more than twice the angle B. The measure of angle C Is five times angle B. Find the angle measures.

Hi Amanda,
The anlge B is the crutial angle since it appears in both facts.

"the measure of angle A is 20 degrees more than twice the angle B"
and
"The measure of angle C Is five times angle B."

Hence I am going to make the angle B the variable.
Let x be the measure of the angle B.
The second fact says that the measure of the angle C is five times x, hence,

angle C is 5 x
The first fact says that the measure of the angle A is 20 degrees plus 2 x, thus
angle A is 20 + 2 x
Since
angle B is x
and the sum of the angles in a triangle is 180 degrees, you should now be able to find x.
Cheers,

Penny