Question

Suppose ∠A and ∠B are complements, while ∠B and ∠C are supplements. If m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1), then m∠A=44, m∠B=46, and m∠C=134. TRUE OR FALSE? Please show your work.

Answer 1

Answer:

TRUE

Step-by-step explanation:

Angle <A and angle <B are complementary, which means their sum must be = 90

Angle <B and angle <C are supplementary which means their sum must be = 180

Now let's see

m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1)

first find the sum of A and B

3x + 17 + 55 - x = 90 add like terms

2x + 72 = 90 subtract 72 from both sides

2x = 18 divide both sides by 2

x = 9

TRUE OR FALSE is asked for

m∠A=44, m∠B=46, and m∠C=134

to find that we just replace c with 9 with every expression given for angles

m<A = 3x + 17

m<A = 3*9 + 17 = 44

m<B =  55 - x

m<B = 55 - 9 = 46

m<C = 134, we don't really need to calculate one by one since the angle are complementary and supplementary.

The answer is TRUE

Answer 2

The statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

∠A and ∠B are complements, while ∠B and ∠C are supplements.

∠A + ∠B = 90 degree

3x + 17 + 55 - x = 90

2x = 18

x = 9

Angle ∠B and angle ∠C are supplementary:

∠B + ∠C = 180

55 -x + 67(x/3  - 1) = 180

x = 9

Put the value of x and find angles A, B, and C.

m∠A = 44

m∠B = 46

m∠C = 134

∠A + ∠B = 90

∠B + ∠C = 180

The above statement is true.

Thus, the statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

Learn more about the angle here:

brainly.com/question/7116550

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