A triangle has an angle that measures 80°. The other two angles are in a ratio of 7:13. What are the measures of those two angles?

The angles are B and C.

The three angles add up to 180º

A=80º

B

C

A+B+C=180º

80º+B+C=180º

B+C=180º-80º

B+C=100º (1)

The ratio between A and B is 7/13; therefore:

B/C=7/13 ⇒B=7C/13 (2)

With the equations (1) and (2), we make a system of equations:

B+C=100

B=7C/13

We can solve this system of equations by substitution method:

7C/13 + C=100

least common multiple=13

7C+13C=1300

20C=1300

C=1300/20

C=65

B=7C/13

B=7*65/13

B=455/13

B=35º

Answer: The measures of those two angles are 65º and 35º.