Two angles, ∠1

Question

and ∠2
, in a diagram are supplementary. If m∠1=77° , what equation can you write to solve for m∠2 ? Let m∠2=x°
(1 point)
Responses

x°=90°−77°
x equals 90 degrees minus 77 degrees

x°=77°
x equals 77 degrees

x°+77°=180°
x plus 77 degrees equals 180 degrees

x°+77°=90°

Answer 1

x plus 77 degrees equals 90 degrees

Answer 2

There are angles whose measures add to 180°
. Their measures are: m∠A=67° , m∠B=(2x+20)° , and m∠C=x° . What is the measure of ∠B ?(1 point)
Responses

62°
62 degrees

31°
31 degrees

180°
180 degrees

82°

Answer 3

82 degrees

Answer 4

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 5

Since ∠D and ∠F are vertical angles, they have the same measure. Therefore, the measure of ∠F is (4x+8)°.

Answer 6

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

124°
124 degrees

132°
132 degrees

48°
48 degrees

31°

Answer 7

The measure of ∠F is (4x+8)°.

Answer 8

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 9

∠A and ∠B are complementary, which means they add up to 90 degrees. Therefore, we can set up the equation:

x + 2x = 90

Combining like terms, we get:

3x = 90

Dividing both sides by 3, we find:

x = 30

Thus, the measure of ∠B is 2x = 2(30) = 60 degrees.