Question

coloring activity
e an equation and solve
2
(2x + 10)°
72°

Explanation:

Step1: Identify angle sum

The angles around the right angle (90°) and the given angles should sum to 180°? Wait, no, looking at the diagram, there's a right angle (90°), a 72° angle, and the angle \((2x + 10)^\circ\). Wait, actually, the three angles: the right angle (90°), 72°, and \((2x + 10)^\circ\) should sum to 180°? Wait, no, maybe it's a full angle? Wait, no, the diagram shows a right angle (the square), a 72° angle, and the angle \((2x + 10)^\circ\) around a point? Wait, no, actually, the right angle is 90°, the 72° angle, and the angle \((2x + 10)^\circ\) should add up to 180°? Wait, no, let's re-examine. The diagram has a vertical line, a line making 72° with the horizontal, and the angle \((2x + 10)^\circ\) with the vertical? Wait, no, the square indicates a right angle (90°), so the sum of the angles \((2x + 10)^\circ\), 90°, and 72°? Wait, no, maybe the three angles around the vertex: the right angle (90°), the 72° angle, and the angle \((2x + 10)^\circ\) should sum to 180°? Wait, no, 90 + 72 + (2x + 10) = 180? Let's check: 90 + 72 is 162, plus (2x + 10) is 172 + 2x = 180? Then 2x = 8, x = 4? Wait, no, maybe I'm wrong. Wait, the right angle is 90°, the angle between the vertical and the other line is 72°? Wait, no, the horizontal line, the right angle (vertical), and the other angle. Wait, maybe the sum of the angles \((2x + 10)^\circ\) and 72° should equal 90°? Because the right angle is 90°, so (2x + 10) + 72 = 90? Let's try that.

Step2: Set up equation

If the two angles \((2x + 10)^\circ\) and \(72^\circ\) are complementary (sum to 90°) because of the right angle, then:
$$(2x + 10) + 72 = 90$$

Step3: Solve for x

Simplify the left side: \(2x + 82 = 90\)
Subtract 82 from both sides: \(2x = 90 - 82 = 8\)
Divide by 2: \(x = \frac{8}{2} = 4\)

Answer:

\(x = 4\)