The strategy involves using the sum of angles in a triangle. For the left triangle, setting up the equation (2x + 20)° + (3x - 2)° = 90° leads to
x = 14.4°. Using this value in the right triangle's angle sum yields 172°.
The strategy is to use the fact that the sum of the angles in a triangle is 180 degrees. We can set up two equations based on this fact, and then solve for x.
First, we can see that the triangle on the left is a right triangle. This means that the sum of the two acute angles in this triangle is 90 degrees. We can write this as an equation:
(2x + 20)° + (3x - 2)° = 90°
Simplifying the left side of this equation, we get:
5x + 18° = 90°
Subtracting 18° from both sides of this equation, we get:
5x = 72°
Dividing both sides of this equation by 5, we get:
x = 14.4°
Now, we can use this value of x to find the measure of the angle at the top of the triangle on the right. We can see that this angle is the sum of the angles (2x + 20)° and 8x°. Substituting x = 14.4° into this expression, we get:
(2 * 14.4°) + 20° + 8 * 14.4°
Simplifying this expression, we get:
36.8° + 20° + 115.2°
= 172°
Therefore, the measure of the angle at the top of the triangle on the right is 172°.
So the answer is x = 14.4°.