<ABC and <JKL are supplementary angles. m<ABC = 3x + 5 and m<JKL = 7x - 25. Find the measure of each angle.
supplementary angles add up to 180
solve: 3x+5 + 7x-25 = 180 for x, then put that value back into each definition.
thanks!
To find the measures of angles ABC and JKL, we need to set up an equation since we know that they are supplementary angles. Supplementary angles add up to 180 degrees.
So, we have the equation:
m<ABC + m<JKL = 180
Substituting the given values for m<ABC and m<JKL:
(3x + 5) + (7x - 25) = 180
Simplifying the equation:
10x - 20 = 180
Adding 20 to both sides:
10x = 200
Dividing both sides by 10:
x = 20
Now that we have found the value of x, we can substitute it back into the expressions for m<ABC and m<JKL to find their values.
m<ABC = 3x + 5 = 3(20) + 5 = 60 + 5 = 65 degrees
m<JKL = 7x - 25 = 7(20) - 25 = 140 - 25 = 115 degrees
Therefore, the measure of angle ABC is 65 degrees and the measure of angle JKL is 115 degrees.