Angles K and O are supplementary. If measurement angle K= 3x+10 and measurement angle O= 10x-12, find the measure of each angle.
I don't understand how to solve.
I assume you know what supplementary means. Thus,
3x+10 + 10x-12 = 180
Find x, and then use that value to determine the angles.
To solve this problem, you'll need to use the fact that the sum of supplementary angles is equal to 180 degrees. Here's the step-by-step process:
1. Start with the given information:
Measurement of angle K = 3x + 10
Measurement of angle O = 10x - 12
2. Since angles K and O are supplementary, their sum is equal to 180 degrees. Write the equation:
(3x + 10) + (10x - 12) = 180
3. Simplify the equation by combining like terms:
3x + 10 + 10x - 12 = 180
13x - 2 = 180
4. Move the constant term to the other side by adding 2 to both sides of the equation:
13x = 182
5. Solve for x by dividing both sides of the equation by 13:
x = 14
6. Substitute the value of x back into the expressions for angle K and angle O:
Measurement of angle K = 3(14) + 10 = 42 + 10 = 52 degrees
Measurement of angle O = 10(14) - 12 = 140 - 12 = 128 degrees
So, angle K measures 52 degrees and angle O measures 128 degrees.