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°+77°=180° x plus 77 degrees equals 180 degrees x°+77°=90° x plus 77 degrees equals 90 degrees x°=90°−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 82° 82 degrees 180° 180 degrees 62° 62 degrees 31°
To find the measure of ∠B, we can set up the equation:
67° + (2x + 20)° + x° = 180°
Combining like terms, we have:
3x + 87° = 180°
Subtracting 87° from both sides, we get:
3x = 93°
Dividing both sides by 3, we find:
x = 31°
So the measure of ∠B is:
2x + 20 = 2(31°) + 20 = 62° + 20 = 82°
Therefore, the measure of ∠B is 82°.
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 48° 48 degrees 31° 31 degrees 132°
If ∠D and ∠E are supplementary angles, their measures add up to 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 that we know x = 31, we can find the measure of ∠D and ∠E:
m∠D = (4x + 8)° = (4 * 31 + 8)° = 132°
m∠E = (x + 17)° = (31 + 17)° = 48°
Since ∠F is a vertical angle with ∠D, it will have the same measure as ∠D. Therefore, the measure of ∠F is 132°.
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 30° 30 degrees 180° 180 degrees 60°
If ∠A and ∠B are complementary angles, their measures add up to 90°. So we can write the equation:
x° + (2x)° = 90°
Combine like terms:
3x = 90
Divide both sides by 3:
x = 30
Now that we know x = 30, we can find the measure of ∠B:
m∠B = (2x)° = (2 * 30)° = 60°
Therefore, the measure of ∠B is 60°.