Solving Unknown Angles Algebraically

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Geometric angles and equations illustration

📐 Part 1: Angle Relationships and Equations

1. Two angles are supplementary. One angle measures 3x + 20°, and the other measures x + 40°. What is the value of x?

Answer: x = _______°

2. In the diagram below, angles A and B are vertically opposite. If angle A = 2y - 15° and angle B = y + 25°, find the measure of both angles.

Angle A = _______° Angle B = _______°

3. Two complementary angles are in the ratio 2:1. If the smaller angle is represented by n, write an equation and solve for n.

Equation: ________________ Answer: n = _______°

4. On a straight line, three adjacent angles measure (x - 10)°, 2x°, and (x + 30)°. Find the value of x and the measure of each angle.

x = _______°

First angle = _______° Second angle = _______° Third angle = _______°

🔍 Part 2: Problem Solving with Multiple Relationships

5. In the diagram, angles around a point are marked as follows: 2a°, (a + 30)°, (3a - 10)°, and 40°. Find the value of a.

Answer: a = _______°

6. Two intersecting lines create four angles. Two opposite angles measure (4m + 15)° and (6m - 25)°. Find the measures of all four angles.

The four angles measure: _______°, _______°, _______°, and _______°

7. In a triangle, the three interior angles are (2p)°, (p + 20)°, and (3p - 14)°. Find the value of p and the measure of each angle.

p = _______°

The three angles measure: _______°, _______°, and _______°

8. Challenge: At the intersection of two streets, four angles are formed. The angles can be expressed as x°, (2x + 10)°, x°, and (2x + 10)°. If one pair of opposite angles is supplementary to an adjacent angle, write and solve the equation to find x.

Equation: ________________ Answer: x = _______°

✍️ Part 3: Reasoning and Explanation

9. Explain in your own words how you would set up an equation to solve for an unknown angle when given supplementary angles. Use an example in your explanation.

10. A student claims that if two angles are vertically opposite, they must be complementary. Is this statement correct? Explain your reasoning with a diagram and mathematical justification.