There are angles whose measures add to 180°

Question

. Their measures are: m∠A=67° , m∠B=(2x+20)° , and m∠C=x° . What is the measure of ∠B ?(1 point)
Responses

180°
180 degrees

82°
82 degrees

62°
62 degrees

31°

Answer 1

To find the measure of ∠B, we can set up an equation that represents the sum of the measures of the angles:

m∠A + m∠B + m∠C = 180°

Substituting the given measures, we have:

67° + (2x+20)° + x° = 180°

Combining like terms, we get:

3x + 87 = 180

Subtracting 87 from both sides, we get:

3x = 93

Dividing both sides by 3, we get:

x = 31

Therefore, the measure of ∠B is given by:

m∠B = 2x + 20 = 2(31) + 20 = 62 + 20 = 82°

So, the measure of ∠B is 82 degrees.

Answer 2

If there are two supplementary angles, ∠D
and ∠E
, where m∠D=(4x+8)° and m∠E=(x+17)° , and ∠F is a vertical angle with ∠D , what is the measure of ∠F ?



(1 point)
Responses

48°
48 degrees

124°
124 degrees

31°
31 degrees

132°

Answer 3

To find the measure of ∠F, we first need to find the value of x.

Since ∠D and ∠E are supplementary angles, their measures add up to 180°:

m∠D + m∠E = 180°
(4x+8)° + (x+17)° = 180°

Combining like terms, we have:
5x + 25 = 180

Subtracting 25 from both sides, we get:
5x = 155

Dividing both sides by 5, we get:
x = 31

Now that we have the value of x, we can substitute it back into the equation to find the measure of ∠D:

m∠D = (4x+8)° = (4(31)+8)° = 132°

Since ∠F is a vertical angle with ∠D, they have the same measure. Therefore, the measure of ∠F is also 132°.

So, the measure of ∠F is 132 degrees.