Two angles, ∠1 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°=77°
x equals 77 degrees
x°=90°−77°
x equals 90 degrees minus 77 degrees
x°+77°=90°
x plus 77 degrees equals 90 degrees
x°+77°=180°
x plus 77 degrees equals 180 degrees
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
82°
82 degrees
180°
180 degrees
31°
To find the measure of ∠B, we need to set up an equation.
Since the measures of the three angles add up to 180 degrees, we can write the equation:
m∠A + m∠B + m∠C = 180
Substituting the given values:
67 + (2x + 20) + x = 180
Combining like terms:
3x + 87 = 180
Solving for x:
3x = 180 - 87
3x = 93
x = 93/3
x = 31
Now we can find the measure of ∠B by substituting the value of x back into the expression (2x + 20):
m∠B = (2 * 31) + 20
m∠B = 62 + 20
m∠B = 82
Therefore, the measure of ∠B is 82 degrees.
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
31°
31 degrees
48°
Since ∠D and ∠E are supplementary angles, their measures add up to 180 degrees. This can be written as:
m∠D + m∠E = 180
Substituting the given expressions:
(4x + 8) + (x + 17) = 180
Simplifying:
5x + 25 = 180
5x = 180 - 25
5x = 155
x = 155/5
x = 31
Now we can find the measure of ∠D by substituting the value of x back into the expression (4x + 8):
m∠D = (4 * 31) + 8
m∠D = 124 + 8
m∠D = 132
Since ∠F is a vertical angle with ∠D, they have the same measure. Therefore, the measure of ∠F is also 132 degrees.
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
90°
90 degrees
180°
180 degrees
60°
60 degrees
30°
Since ∠A and ∠B are complementary angles, their measures add up to 90 degrees. This can be written as:
m∠A + m∠B = 90
Substituting the given expressions:
x + 2x = 90
3x = 90
x = 90/3
x = 30
Now we can find the measure of ∠B by substituting the value of x back into the expression (2x):
m∠B = 2 * 30
m∠B = 60
Therefore, the measure of ∠B is 60 degrees.