∠MAT and ∠TAH are supplementary angles. The angles have the following measures: ∡MAT=(6x−6)° and ∡TAH=(4x−14)° . What is an equation to solve for x ?(1 point) Responses A.x°−20°=180° B.10x° 20°=180° C.9x°−20°=180°D. 10x°−20°=180°.
In order to find an equation to solve for x, we need to set up an equation using the given information that ∠MAT and ∠TAH are supplementary angles.
Since two supplementary angles add up to 180 degrees, we can write the equation as:
∠MAT + ∠TAH = 180
Substituting the measures of the angles, we get:
(6x - 6) + (4x - 14) = 180
Simplifying, we have:
10x - 20 = 180
Rearranging the equation to isolate x, we have:
10x = 200
Dividing both sides of the equation by 10, we get:
x = 20
Therefore, the equation to solve for x is:
D. 10x° - 20° = 180°
Use facts about supplementary angles to solve the following problem. Two angles are supplementary and have measures m∠ABC=15° and m∠CBD=x° . What is the value of m∠CBD ?(1 point) Responses 165° 165 degrees 15° 15 degrees 75° 75 degrees 180°
Since two angles are supplementary, their measures add up to 180 degrees. Thus, we can write the equation:
m∠ABC + m∠CBD = 180
Substituting the given measures, we have:
15 + x = 180
Simplifying the equation, we subtract 15 from both sides:
x = 165
Therefore, the value of m∠CBD is 165 degrees.
The correct response is: 165°
∠ACB and ∠BCD are supplementary angles. The angles have the following measures: ∡ACB=(x 28)° and ∡BCD=(x 48)° . What is m∠BCD ?(1 point) Responses 80° 80 degrees 100° 100 degrees 128° 128 degrees 52°
Since ∠ACB and ∠BCD are supplementary angles, their measures add up to 180 degrees. Thus, we can write the equation:
∠ACB + ∠BCD = 180
Substituting the given measures, we have:
(x + 28) + (x + 48) = 180
Simplifying the equation, we combine like terms:
2x + 76 = 180
Next, we isolate the term with x by subtracting 76 from both sides:
2x = 104
Finally, we divide both sides by 2 to solve for x:
x = 52
Since we know that ∠BCD = (x + 48)°, we substitute the value of x:
∠BCD = (52 + 48)°
∠BCD = 100°
Therefore, the measure of ∠BCD is 100 degrees.
The correct response is: 100°.