Complementary and Supplementary Angles |Complementary Angles ... - Free Printable

We are given a straight line PQ with point O on it. From point O, two rays OS and OR go upward, forming three angles along the straight line:

- Angle POS = 5x + 4°
- Angle SOR = x - 2°
- Angle ROQ = 3x + 7°

Since PQ is a straight line, the total angle from P to Q through O must be 180 degrees.

So we can write an equation:

> (5x + 4) + (x - 2) + (3x + 7) = 180

Now let’s combine like terms step by step.

First, add all the x terms:
5x + x + 3x = 9x

Then add all the constant numbers:
4 - 2 + 7 = 9

So the equation becomes:

> 9x + 9 = 180

Now subtract 9 from both sides:

> 9x = 171

Now divide both sides by 9:

> x = 19

Let’s double-check by plugging x = 19 back into each angle:

- 5x + 4 = 5(19) + 4 = 95 + 4 = 99°
- x - 2 = 19 - 2 = 17°
- 3x + 7 = 3(19) + 7 = 57 + 7 = 64°

Add them up: 99 + 17 + 64 = 180° → Perfect! It checks out.

Final Answer:
19