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

Answer 1

To find the measure of angle B, we can set up an equation using the fact that the three angles add up to 180°.

m∠A + m∠B + m∠C = 180°
67° + (2x + 20)° + x° = 180°
67° + 2x + 20° + x° = 180°
3x + 87° = 180°
3x = 93°
x = 31°

Now that we have found the value of x, we can plug it back into the expression for angle B:

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

Therefore, the measure of angle B is 82°.

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 ?

Answer 3

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

m∠D + m∠E = 180°
(4x + 8)° + (x + 17)° = 180°
4x + 8 + x + 17 = 180
5x + 25 = 180
5x = 155
x = 31

Now that we have found the value of x, we can find the measures of ∠D and ∠E:

m∠D = 4x + 8
m∠D = 4(31) + 8
m∠D = 124 + 8
m∠D = 132°

m∠E = x + 17
m∠E = 31 + 17
m∠E = 48°

Since ∠F is a vertical angle with ∠D, ∠F is also 132°.

Therefore, the measure of ∠F is 132°.

Answer 4

In a geometric diagram, ∠A and ∠B are complementary, and they form a straight line with ∠C . If m∠A=x° , m∠B=(2x)° , and m∠C=90° , what is the measure of ∠B ?(1 point)
Responses

Answer 5

Since angles A and B are complementary, their measures add up to 90°:

m∠A + m∠B = 90°
x + 2x = 90
3x = 90
x = 30

Now that we have found the value of x, we can find the measure of angle B:

m∠B = 2x
m∠B = 2(30)
m∠B = 60°

Therefore, the measure of angle B is 60°.