A quadrilateral has two angles that measure 110° and 85°. The other two angles are in a ratio of 14:19. What are the measures of those two angles?

Question

A quadrilateral has two angles that measure 110° and 85°. The other two angles are in a ratio of 14:19. What are the measures of those two angles?

Answer 1

The angles of a quadrilateral add up to 360 degrees.

The first two angles (110 and 85) add up to 195 degrees.

If all four add up to 360, then the two remaining angles add up to 360 - 195 = 165 degrees.

We'll call our missing angles x and y.

We know that they add up to 165, so

x + y = 165

We also know that the ratio of the two angles is 14:19. We can also write this as 14/19, so x/y = 14/19.

It doesn't matter which order the x and y are in, because it doesn't matter which angle is x and which is y.

In this case, the smaller angle is x.

We now have two equations and two unknowns. Let's solve for x in the second equation by multiplying both sides by y. Now our two equations are:

x + y = 165

x = (14/19)*y

We can substitute (14/19)*y into our first equation for x:

(14/19)*y + y = 165

(33/19)* y = 165

Multiply both sides by 19/33 to get y=95

We can plug that into either equation to solve for x:

x + 95 = 165

x = 70

The two angles are 70 degrees and 95 degrees