Exterior Angle Theorem Worksheet
Grade 10 Math worksheet on the Exterior Angle Theorem, including definitions, problem-solving, and applications.
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Exterior Angle Theorem
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
In the triangle above, ∠ACD is an exterior angle. Its remote interior angles are ∠ABC and ∠BAC. Therefore, m∠ACD = m∠ABC + m∠BAC (or z = x + y).
1. Which of the following statements correctly defines the Exterior Angle Theorem?
The sum of the interior angles of a triangle is 180°.
An exterior angle is equal to the sum of its two adjacent interior angles.
An exterior angle is equal to the sum of its two remote interior angles.
All angles in an equilateral triangle are 60°.
2. In a triangle, if two interior angles are 50° and 70°, what is the measure of the exterior angle adjacent to the third interior angle?
60°
120°
130°
180°
3. Consider a triangle ABC. If the measure of angle A is 45° and the measure of angle B is 75°, what is the measure of the exterior angle at vertex C?
4. In the diagram above, find the value of x.
5. The exterior angle of a triangle is always than either of its remote interior angles.
6. If an exterior angle of a triangle measures 110° and one of its remote interior angles measures 60°, the other remote interior angle must measure .
7. A triangle has interior angles measuring (2x + 10)°, (3x - 5)°, and (x + 35)°. Find the value of x and then determine the measure of each interior angle and one exterior angle.
8. The sum of an interior angle and its adjacent exterior angle is always 180°.
True
False
9. An exterior angle can be smaller than one of its remote interior angles.
True
False