Geometry Test Questions on Exterior and Remote Interior Angles

📐 Quick Study Guide

🔍 Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
• ✏️ Formula: $ \angle{a} = \angle{b} + \angle{c} $ where $ \angle{a} $ is the exterior angle and $ \angle{b} $ and $ \angle{c} $ are the remote interior angles.
• 💡 Remote Interior Angles: These are the two angles inside the triangle that are not adjacent to the exterior angle.
• 🧭 Supplementary Angles: Exterior angle and its adjacent interior angle are supplementary (they add up to 180 degrees).
• ➕ Sum of Interior Angles: The sum of the three interior angles of any triangle is always 180 degrees.

✍️ Practice Quiz

1. What is the measure of an exterior angle of a triangle if its remote interior angles measure 30° and 70°?
   1. 40°
   2. 100°
   3. 140°
   4. 25°
2. If an exterior angle of a triangle measures 120° and one of its remote interior angles measures 50°, what is the measure of the other remote interior angle?
   1. 60°
   2. 70°
   3. 80°
   4. 90°
3. An exterior angle and its adjacent interior angle form what type of angle pair?
   1. Complementary
   2. Supplementary
   3. Vertical
   4. Corresponding
4. Which theorem directly relates an exterior angle of a triangle to its two remote interior angles?
   1. Pythagorean Theorem
   2. Triangle Inequality Theorem
   3. Exterior Angle Theorem
   4. Angle Bisector Theorem
5. If two remote interior angles are equal and the exterior angle measures 84°, what is the measure of each remote interior angle?
   1. 21°
   2. 42°
   3. 63°
   4. 168°
6. The three interior angles of a triangle add up to:
   1. 90°
   2. 180°
   3. 270°
   4. 360°
7. An exterior angle of a triangle is always:
   1. Acute
   2. Obtuse
   3. Equal to one of the remote interior angles
   4. Equal to the sum of the two remote interior angles