Quiz – Two Exterior Angles are Equal at a Vertex

Test your understanding of this quick proof.

Try to answer the questions before checking the answers at the bottom of the page.

Question 1

Interior angle \(= 70^\circ\)

Find the exterior angle.

A) \(100^\circ\)
B) \(110^\circ\)
C) \(120^\circ\)

Question 2

Interior angle \(= 60^\circ\)

Find both exterior angles.

A) \(100^\circ\)
B) \(110^\circ\)
C) \(120^\circ\)

Question 3

Interior angle \(= x\)
Exterior angle \(= x + 20\)

Find \(x\).

A) \(70^\circ\)
B) \(80^\circ\)
C) \(90^\circ\)

Question 4

Interior angle \(= x\)
Exterior angle \(= 2x − 10\)

Find \(x\).

A) \(60^\circ\)
B) \(70^\circ\)
C) \(80^\circ\)

Question 5

Why are the two exterior angles equal?

A) Because they are interior angles
B) Because they form linear pairs with the same angle
C) Because they are adjacent angles

Question 6

The interior angle at a vertex is \(95^\circ\).

Find each exterior angle at that vertex.

A) \(85^\circ\)
B) \(95^\circ\)
C) \(105^\circ\)

Question 7

Each exterior angle at a vertex is \(130^\circ\).

What is the interior angle?

A) \(40^\circ\)
B) \(60^\circ\)
C) \(50^\circ\)

Question 8

The interior angle is \(x\).

Each exterior angle is \(3x+20^\circ\).

Find \(x\).

A) \(30^\circ\)
B) \(40^\circ\)
C) \(50^\circ\)

Question 9

The interior angle is \(\text{Angle 3}\). The two exterior angles are \(\text{Angle 4}\) and \(\text{Angle 5}\).

If:
\(\text{Angle 3}+\text{Angle 4}=180^\circ\)

and:


\(\text{Angle 3}+\text{Angle 5}=180^\circ,\)

what can we conclude?

A) \(\text{Angle 4} = \text{Angle 5}\)
B) \(\text{Angle 3} = \text{Angle 4}\)
C) \(\text{Angle 3} = \text{Angle 5}\)

Question 10

One exterior angle at a vertex is \(125^\circ\).

What are the interior angle and the other exterior angle?

A) Interior angle \(=125^\circ\), other exterior angle \(=55^\circ\)
B) Interior angle \(=65^\circ\), other exterior angle \(=115^\circ\)
C) Interior angle \(=55^\circ\), other exterior angle \(=125^\circ\)

Answers

  1. B – \(110^\circ\)
  2. C – \(120^\circ\)
  3. B – \(80^\circ\)
  4. B – \(70^\circ\)
  5. B – Because they form linear pairs with the same angle
  6. A – \(85^\circ\)
  7. C – \(50^\circ\)
  8. B – \(40^\circ\)
  9. A – \(\text{Angle 4} = \text{Angle 5}\)
  10. C – Interior angle \(=55^\circ\), other exterior angle \(=125^\circ\)

Practice

  • Take the Quiz (Current page)

Continue Learning

  1. Sum of Exterior Angles of a Triangle (Proof)
  2. Exterior Angle Theorem of a Triangle
  3. Two Exterior Angles at a Vertex are Equal (Proof)
  4. Two Exterior Angles are Equal at a Vertex (Quick Proof)

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