Question

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?

Answer 1

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.