219k views
1 vote
One angle of a triangle measures 100°. The other two angles are in a ratio of 5:11. What are the measures of those two angles?

1 Answer

3 votes

Answer:

Explanation:

Let x be the measure of the smaller angle, and y be the measure of the larger angle. Then we know that:

x + y + 100 = 180, since the sum of the angles in a triangle is 180 degrees.

y/x = 11/5, since the other two angles are in a ratio of 5:11.

We can use the second equation to solve for y in terms of x:

y/x = 11/5

y = 11x/5

Substituting this into the first equation, we get:

x + (11x/5) + 100 = 180

Multiplying both sides by 5, we get:

5x + 11x + 500 = 900

16x = 400

x = 25

Therefore, the smaller angle measures 25 degrees, and the larger angle measures:

y = 11x/5 = 11(25)/5 = 55

So the two angles are 25 degrees and 55 degrees.

To check this make sure the sum of all the angles is 180.

55+25+100=180

User Martin Gal
by
8.5k points