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°=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°
x plus 77 degrees equals 90 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
31°
31 degrees
180°
180 degrees
82°
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 ?
Since ∠D and ∠F are vertical angles, they have the same measure. Therefore, the measure of ∠F is (4x+8)°.
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°
The measure of ∠F is (4x+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
∠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.