A triangle has an angle that measures 148°. The other two angles are in a ratio of 7:9. What are the measures of those two angles?

Answer 1

In this problem, please pay attention that every time the ratio of two of three angles are given use the rationale that 7:9 , means 7x and 9x because the angles are unknown or the is a total 16 parts. (7+9)=16

1. A +B +C =180. the sam° of the angles on a triangles is equal to 180°
2. 148°+7x+9x= 180. substitute the unknown angles in the equation
3. 148°+16x°=180 grouping like terms
4. 16x= 180 -148 subtracting
5. 16x=32 Dividing both sides by 16
6. x=2
7. Substitute the x value into the ratio provided 7(2) =14, 9(2)=18. So the the measure of this two angles are 14+18= 32°
8. To verify your findings: 7:9. = 7/9 =0.77777. and 14/18 = 0.77777, so the ratio or proportion is the same.

Answer 2

The sum of the 2 other angles is 32.

A ratio of 7:9 means there are 16 total parts, i.e. each angle is a multiple of 2,namely 14 and 18.

Alternatively, you could solve this as x:32-x = 7:9, i.e. 7(32-x)=9x.