Question

The measure of an angle is six more than twice its complement. What is the measure of the larger angle? How did you get your answer?

Answer 1

The larger angle measures 62 degrees. This was found by setting up an equation where the angle is defined as six more than twice its complement, then solving for the angle itself.

Step-by-step explanation:

To solve the problem where the measure of an angle is six more than twice its complement, we need to use the relationship between complementary angles. Complementary angles are two angles that add up to 90 degrees. If we denote one angle as x, then its complement is 90 - x. According to the problem statement, the measure of the angle can be expressed as 2(90 - x) + 6.

Setting up the equation, we have x = 2(90 - x) + 6. Simplifying, x = 180 - 2x + 6, which leads us to 3x = 186. Dividing both sides by 3, we get x = 62 degrees. Therefore, the measure of the larger angle is 62 degrees.

The steps we followed were:

1. Express the angle in terms of its complement.
2. Set up and simplify the equation.
3. Solve for x.
4. Find the measure of the angle.