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=180°−39°
x equals 180 degrees minus 39 degrees
m∠6+39°=180°
x plus 39 degrees equals 180 degrees
m∠6=39°
x equals 39 degrees
m∠6+39°=90°
m∠6=180°−39°
wo 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°=180°
x plus 77 degrees equals 180 degrees
x°+77°=90°
x plus 77 degrees equals 90 degrees
x°=90°−77°
x equals 90 degrees minus 77 degrees
x°=77°
x°+77°=180°
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
31°
31 degrees
180°
180 degrees
82°
82 degrees
62°
m∠B=(2x+20)°
We are given that the measures of angles A, B, and C add up to 180°.
So, we can write the equation:
67° + (2x + 20)° + x° = 180°
To solve for the measure of angle B, we need to solve this equation.
ok then solve it
To solve the equation:
67° + (2x + 20)° + x° = 180°
Combine like terms:
3x + 87° = 180°
Subtract 87° from both sides:
3x = 93°
Divide both sides by 3:
x = 31°
Now, substitute the value of x 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°.
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Question
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
31°
31 degrees
132°
132 degrees
48°
48 degrees
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Since angles D and E are supplementary, their sum is 180°.
So we can write the equation:
(4x + 8)° + (x + 17)° = 180°
Combine like terms:
5x + 25° = 180°
Subtract 25° from both sides:
5x = 155°
Divide both sides by 5:
x = 31°
Now, we need to find the measure of angle F, which is a vertical angle with angle D.
So the measure of angle F is equal to the measure of angle D:
m∠F = m∠D = (4x + 8)° = (4(31°) + 8)° = 124°
Therefore, the measure of angle F is 124°.
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
180°
180 degrees
90°
90 degrees
60°
60 degrees
30°