Question

A quadrilateral has two angles that measure 115° and 75°. The other two angles are in a

ratio of 2:15. What are the measures of those two angles?

Answer 1

We have two angles measuring 115° and 75°. Let's call the other two angles "x" and "y." According to the problem, their ratio is 2:15.

So, we can set up an equation:

x/y = 2/15

Now, we know that the sum of the angles in a quadrilateral is 360 degrees. Therefore:

115 + 75 + x + y = 360

Simplify the equation:

190 + x + y = 360

Now, let's solve for x and y:

x + y = 360 - 190

x + y = 170

We also have the ratio:

x/y = 2/15

We can use this ratio to express one of the variables in terms of the other:

x = (2/15) * y

Now, substitute this into the equation x + y = 170:

(2/15) * y + y = 170

Multiply both sides by 15 to eliminate the fraction:

2y + 15y = 170 * 15

Combine like terms:

17y = 2550

Now, divide by 17 to find y:

y = 2550 / 17

y ≈ 150

Now that we know the value of y, we can find x using the ratio:

x = (2/15) * y

x = (2/15) * 150

x = 20

So, the correct measures of the two angles are x = 20 degrees and y = 150 degrees.