1. Identify the following pairs of angles as complementary, supplementary, or equal.
a. 15° and 75°
b. 133° and 133°
c. 90° and 90°
d. 45° and 5°
a. 15° and 75°: Complementary (15° + 75° = 90°)
b. 133° and 133°: Supplementary (133° + 133° = 266°, which is not 180°, so this is incorrect; they are not supplementary. They are equal if they are the same angle, but here they are two different angles of the same measure, so they are equal)
c. 90° and 90°: Equal (both are 90°)
d. 45° and 5°: Neither (45° + 5° = 50°, not 90° or 180°)
2. Find the measure of x in the following figures.
a. The figure shows two angles formed by intersecting lines: 42° and x. Since they are vertical angles, they are equal. Therefore, x = 42°.
b. The figure shows two angles on a straight line: x + 105° and x. The sum of angles on a straight line is 180°. So, (x + 105°) + x = 180°. Solving for x: 2x + 105° = 180°, 2x = 75°, x = 37.5°.
c. The figure shows three angles around a point: 90°, x/2, and x. The sum of angles around a point is 360°. So, 90° + x/2 + x = 360°. Solving for x: 90° + 1.5x = 360°, 1.5x = 270°, x = 180°.
3. An angle is 30° less than two times its supplement. Find the angles.
Let the angle be x. Its supplement is 180° - x. According to the problem, x = 2(180° - x) - 30°. Solving for x: x = 360° - 2x - 30°, x + 2x = 330°, 3x = 330°, x = 110°. The supplement is 180° - 110° = 70°.
4. Find the value of x from the given figure below.
The figure shows three angles around a point: x° + 15°, x°, and x° + 34°. The sum of angles around a point is 360°. So, (x + 15) + x + (x + 34) = 360. Simplifying: 3x + 49 = 360, 3x = 311, x = 103.67° (approximately).
5. Check whether k is parallel to m in the given figure.
The figure shows two lines, k and m, intersected by a transversal. The angles formed are 50° and 120°. The angle 50° is on the top right of line k, and the angle 120° is on the bottom left of line m. These are alternate interior angles. For lines to be parallel, alternate interior angles must be equal. Since 50° ≠ 120°, k is not parallel to m.
Parent Tip: Review the logic above to help your child master the concept of angles and lines worksheet.
