Question

The measures of two supplementary angles have a ratio of 4:5. What is the measure of the larger angle?

Answer 1

Answer:

80° and 100°

Step-by-step explanation:

If both angle are supplementary, that means theis sum is equal to 180°.

The given ratio of such angles is 4:5, which means the if one is quadraple, the other one is five times the angle.

We just have to find to numbers that are in the same ratio of 4:5 and sum 180°, those angles are 80 and 100, because both numbers can be obtained by multiplying the same number to the ratio.

Notice that if you multiply each part of the ratio by 20, they will sum 180°.

Therefore, the angles are 80° and 100°.

Answer 2

First, we know that all supplementary angles add to 180°. Then, since the angles are in the ratio 4:5, we can also represent these angles as 4x and 5x respectively. Both angle measures have the same variable (x) because no matter how large the angles are, they must have a common multiple because they are in a ratio. We can then write the formula 4x+5x=180 and solve for x. First, you combine like terms to get 9x=180. The you divide both sides by 9 to get x=20. Then, we can find both angles to be 80 (4*20) and 100 (5*20) by plugging them into 4x and 5x. Since 100 is larger, that is your answer.

I hope this helps.