There are two complementary angles, ∠5 and ∠6 . If m∠5=39° , what equation can you write to solve for m∠6 ?(1 point)
Responses
m∠6+39°=180°
x plus 39 degrees equals 180 degrees
m∠6+39°=90°
x plus 39 degrees equals 90 degrees
m∠6=180°−39°
x equals 180 degrees minus 39 degrees
m∠6=39°
11 answers
x equals 39 degrees
pick the correct response
m∠6=180°−39°
x equals 180 degrees minus 39 degrees
x equals 180 degrees minus 39 degrees
Two angles, ∠1
∠
1
and ∠2
∠
2
, in a diagram are supplementary. If m∠1=77° , what equation can you write to solve for m∠2 ? Let m∠2=x°
�
∠
2
=
�
°
(1 point)
Responses
x°+77°=90°
x plus 77 degrees equals 90 degrees
x°=77°
x equals 77 degrees
x°+77°=180°
x plus 77 degrees equals 180 degrees
x°=90°−77°
∠
1
and ∠2
∠
2
, in a diagram are supplementary. If m∠1=77° , what equation can you write to solve for m∠2 ? Let m∠2=x°
�
∠
2
=
�
°
(1 point)
Responses
x°+77°=90°
x plus 77 degrees equals 90 degrees
x°=77°
x equals 77 degrees
x°+77°=180°
x plus 77 degrees equals 180 degrees
x°=90°−77°
x plus 77 degrees equals 180 degrees
There are angles whose measures add to 180°
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
31°
31 degrees
180°
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
31°
31 degrees
180°
m∠A + m∠B + m∠C = 180°
67° + (2x + 20)° + x° = 180°
3x + 87° = 180°
3x = 180° - 87°
3x = 93°
x = 93° / 3
x = 31°
To find the measure of ∠B, substitute x = 31° into the equation:
m∠B = 2x + 20°
m∠B = 2(31°) + 20°
m∠B = 62° + 20°
m∠B = 82°
Therefore, the measure of ∠B is 82 degrees.
67° + (2x + 20)° + x° = 180°
3x + 87° = 180°
3x = 180° - 87°
3x = 93°
x = 93° / 3
x = 31°
To find the measure of ∠B, substitute x = 31° into the equation:
m∠B = 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
48°
48 degrees
31°
31 degrees
124°
124 degrees
132°
∠
�
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
31°
31 degrees
124°
124 degrees
132°
Since ∠D and ∠E are supplementary, their measures add up to 180°:
m∠D + m∠E = 180°
(4x + 8)° + (x + 17)° = 180°
5x + 25° = 180°
5x = 180° - 25°
5x = 155°
x = 155° / 5
x = 31°
Now, to find the measure of ∠F, we can use the fact that vertical angles are congruent. So, ∠F has the same measure as ∠D:
m∠F = m∠D = (4x + 8)°
m∠F = 4(31°) + 8°
m∠F = 124° + 8°
m∠F = 132°
Therefore, the measure of ∠F is 132 degrees.
m∠D + m∠E = 180°
(4x + 8)° + (x + 17)° = 180°
5x + 25° = 180°
5x = 180° - 25°
5x = 155°
x = 155° / 5
x = 31°
Now, to find the measure of ∠F, we can use the fact that vertical angles are congruent. So, ∠F has the same measure as ∠D:
m∠F = m∠D = (4x + 8)°
m∠F = 4(31°) + 8°
m∠F = 124° + 8°
m∠F = 132°
Therefore, the measure of ∠F is 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
60°
60 degrees
180°
180 degrees
30°
30 degrees
90°
Responses
60°
60 degrees
180°
180 degrees
30°
30 degrees
90°
Since ∠A and ∠B are complementary angles, their measures add up to 90°:
m∠A + m∠B = 90°
x° + (2x)° = 90°
3x° = 90°
x° = 90° / 3
x° = 30°
Therefore, the measure of ∠B is 2x°:
m∠B = (2x)° = 2(30°) = 60°
So, the measure of ∠B is 60 degrees.
m∠A + m∠B = 90°
x° + (2x)° = 90°
3x° = 90°
x° = 90° / 3
x° = 30°
Therefore, the measure of ∠B is 2x°:
m∠B = (2x)° = 2(30°) = 60°
So, the measure of ∠B is 60 degrees.
11 answers