To find the equation to solve for x, we need to use the fact that the sum of the angle measures is equal to 180°.
We can set up the equation as follows:
(m∠ABC) + (m∠CBD) + (m∠DBE) = 180°
Substituting the given angle measures, we have:
(x - 6) + (4x - 14) + (5x) = 180°
Now we can solve for x by combining like terms:
10x - 20 = 180°
Adding 20 to both sides:
10x = 200°
Finally, we divide both sides by 10 to solve for x:
x = 20°
Three angles have measures that add to 180°
180
°
. They have the following angle measures: m∠ABC=(x−6)° , m∠CBD=(4x−14)° , and m∠DBE=5x° . What is the equation to solve for x ?
7 answers
Two supplementary angles have the following measures: m∠ABC=135° and m∠CBD=9x° . What is the equation to solve for x ?
To find the equation to solve for x, we know that two angles are supplementary if their measures add up to 180 degrees.
We can set up the equation as follows:
m∠ABC + m∠CBD = 180°
Substituting the given angle measures, we have:
135° + 9x° = 180°
Now we can solve for x by isolating the variable on one side of the equation:
9x° = 180° - 135°
9x° = 45°
Dividing both sides of the equation by 9:
x° = 45°/9
x° = 5°
Therefore, the equation to solve for x is 9x = 45.
We can set up the equation as follows:
m∠ABC + m∠CBD = 180°
Substituting the given angle measures, we have:
135° + 9x° = 180°
Now we can solve for x by isolating the variable on one side of the equation:
9x° = 180° - 135°
9x° = 45°
Dividing both sides of the equation by 9:
x° = 45°/9
x° = 5°
Therefore, the equation to solve for x is 9x = 45.
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
∠
?
∠
?
Since the two angles are supplementary, their measures add up to 180 degrees.
We can set up the equation as follows:
m∠ABC + m∠CBD = 180°
Substituting the given angle measures, we have:
15° + x° = 180°
Now we can solve for x by isolating the variable on one side of the equation:
x° = 180° - 15°
x° = 165°
Therefore, the value of ∠CBD is 165 degrees.
We can set up the equation as follows:
m∠ABC + m∠CBD = 180°
Substituting the given angle measures, we have:
15° + x° = 180°
Now we can solve for x by isolating the variable on one side of the equation:
x° = 180° - 15°
x° = 165°
Therefore, the value of ∠CBD is 165 degrees.
Two angles are supplementary and have measures m∠QRS=(x+40)° and m∠SRT=x° . What is the measure of ∠QRS ?
Since the two angles are supplementary, their measures add up to 180 degrees.
We can set up the equation as follows:
m∠QRS + m∠SRT = 180°
Substituting the given angle measures, we have:
(x + 40)° + x° = 180°
Now we can solve for x by combining like terms:
2x + 40° = 180°
Subtracting 40° from both sides:
2x = 140°
Finally, we divide both sides by 2 to solve for x:
x = 70°
Therefore, the measure of ∠QRS is:
m∠QRS = x + 40° = 70° + 40° = 110°
We can set up the equation as follows:
m∠QRS + m∠SRT = 180°
Substituting the given angle measures, we have:
(x + 40)° + x° = 180°
Now we can solve for x by combining like terms:
2x + 40° = 180°
Subtracting 40° from both sides:
2x = 140°
Finally, we divide both sides by 2 to solve for x:
x = 70°
Therefore, the measure of ∠QRS is:
m∠QRS = x + 40° = 70° + 40° = 110°