Is there a way to get help with the question below with details of solving?

Question

If the measure of ∠A is 100° more than three times the measure of ∠B, and the sum of the measures of the two angles is 180°, what is the measure of each angle?

m(∠A) =

m(∠B) =

Answer 1

The two angles are supplementary angles as both add up to the sum of 180 degrees

Let x represent the measurement of Angle B.

Angle A can be expressed as 3x+100

Angle B can be expressed as x

We are told the sum of angle A and Angle B is equal to 180

So we can express that as an equation and solve for x

Angle A + Angle B = 180, using what is given from the problem we say.

3x + 100 + x = 180

Combine the x’s

3x + x = 4x

So we have 4x + 100 = 180

Subtract 100 from both sides

4x = 80

Now divide both sides by 4

X = 80/4 or 20 degrees

Angle B = 20 degrees

Angle A = 3(20) + 100 = 60 + 100 = 160 degrees.

I hope this helps. If you need any further clarification please feel free to ask. Have a wonderful day.

Michaela

Answer 2

We represent three times the measure of angle B as 3B.

According to the problem, we can write one equation as follows:

A=100+3B

The problem also states that the sum of angles A and B is 180 degrees,

thus, we can write another equation: A+B=180

We have now two equations with two unknowns, A and B

From the last equation, A+B=180, we can subtract A to both sides of the equal sign, and we get the new expression: B=180-A

The next step is to substitute the value of B in the equation A=100+3B

Hence,

A=100+3(180-A)

Applying the distributive property:

A=100+3x180-3xA = 100+540-3A=640-3A

Therefore, we have the equation A=640-3A, and we can solve for A

We first add 3A to both sides of the equal sign.

4A=640

Secondly, we divide both sides of the equal sign by 4 in order to isolate A

A=640/4 =160 degrees

Since B=180-A, we have B=180-160=20 degrees

Therefore, our solution is:

A=160 degrees

B=20 degrees

Let’s verify it.

Three times our angle B is 3B=3x20=60 degrees

Is A=100 +3B? substituting 3B for 60, we’ve got A=100+60=160 degrees

Clearly, it verifies our solution.