A figure shows two nonadjacent angles with measures (2x + 3) and 2x. If the angles are complementary , what is the equation for the angle measures?
(__) + 2x = __
(2x + 3) + 2x = 90
Two complementary angles have measures (2x) and (3x) . What is the value of x and the two angle measures?
x = ___, (2x) = ___ , and (3x) = ___
To find the value of x, we can set up the equation:
(2x) + (3x) = 90
Combine like terms:
5x = 90
Divide both sides by 5:
x = 18
Plug in the value of x to find the angle measures:
(2x) = 2(18) = 36
(3x) = 3(18) = 54
So, x = 18, (2x) = 36, and (3x) = 54.
are you sure?
Apologies for the confusion earlier. Let's solve the equation correctly:
(2x) + (3x) = 90
Combine like terms:
5x = 90
Divide both sides by 5:
x = 18
Plug in the value of x to find the angle measures:
(2x) = 2(18) = 36
(3x) = 3(18) = 54
So, x = 18, (2x) = 36, and (3x) = 54.
Angles j and k are supplementary angles. What is m<j if m<k = 117
If angles j and k are supplementary, it means that the sum of their measures is equal to 180 degrees.
Given that m<k = 117, we can set up an equation:
m<j + 117 = 180
Subtract 117 from both sides:
m<j = 180 - 117
Simplifying:
m<j = 63 degrees
So, the measure of angle j is 63 degrees.
Two supplementary angles have measures m<ABC = 105 and m<CBD = (3x - 24) . What is the equation to solve for x?
(3x - 24) + ___ = ____
If angles ABC and CBD are supplementary, their measures add up to 180 degrees.
We are given that m<ABC = 105 and m<CBD = (3x - 24).
The equation to solve for x would be:
105 + (3x - 24) = 180
Simplifying:
3x - 24 + 105 = 180
Combine like terms:
3x + 81 = 180
Subtract 81 from both sides:
3x = 99
Divide both sides by 3:
x = 33
Now we can substitute the value of x back into the equation:
(3x - 24) + ___ = ____
(3(33) - 24) + ___ = ____
(99 - 24) + ___ = ____
75 + ___ = ____
So, the equation to solve for x is (3x - 24) + 75 = ____.