Question

angle a and b are both supplementary to angle c if the measure of angle a is 12 less than 2 times the measure of c find the measure of b

Answer 1

The measure of a = b = 116 degrees

Explanation:

Here, we have value of angles to calculate.

If a and b are both supplementary to c, what this means is that when we add either a or b to c, we get 180

Hence; Mathematically;

a + c = 180 and b + c = 180

What we have here is that a and b must be equal since they are both supplementary to the same angle value

Now, we are told further in the question that the measure of angle a is 12 less than 2 times the measure of c;

Mathematically, this means that;

a = 2c - 12

So we now want to find the measure of b

Let’s substitute for a

2c -12 + c = 180

3c -12 = 180

3c = 180 + 12

3c =192

c = 192/3

c = 64

Thus; a = 2c - 12 = 2(64) -12 = 128 -12 = 116