Answer:
x = 10
Explanation:
We know the following pieces of information:
- supplementary angles add to 180°
- the measures of the interior angles of a triangle add 180°
First, we can solve for the unknown interior angle (which we can call y) measure in terms of x using the fact that it is supplementary with the angle marked (10x + 20):
(10x + 20) + y = 180
y = 180 - 10x - 20
y = 160 - 10x
Then, we can set the sum of the triangle's interior angle measures to 180 and solve for x:
y + (7x + 20) + 30 = 180
↓ substituting in the solution for y in terms of x
(160 - 10x) + (7x + 20) + 30 = 180
↓ grouping like terms
(160 + 20 + 30) + (-10x + 7x) = 180
↓ combining like terms
210 - 3x = 180
↓ adding 3x to both sides
210 = 180 + 3x
↓ subtracting 180 from both sides
30 = 3x
↓ dividing both sides by 3
10 = x