Solved Examples of Consecutive Interior Angles
Example 1: If transversal cuts two parallel lines and a pair of successive interior angles measure (4x + 8)° and (16x + 12)°, calculate the value of x and the value of both consecutive interior angles.
Solution:
Because the supplied lines are parallel, the inner angles (4x + 8)° and (16x + 12)° are consecutive. These angles are additional according to the consecutive interior angle theorem.
As a result, (4x + 8)° + (16x + 12)° = 180°
⇒ 20x + 20 = 180°
⇒ 20x = 180° – 20°
⇒ 20x = 160°
⇒ x = 8°
Let us now substitute x for the values of the subsequent interior angles.
Thus, 4x + 8 = 4(8) + 8 = 40° and
16x + 12 = 16(8) + 12 = 140°
Thus, value of both consecutive interior angles 40° and 140°.
Example 2: The value of ∠3 is 85° and ∠6 is 110°. Now, check the ‘n’ and ‘m’ lines are parallel.
Solution:
If the angles 110° and 85° in the above figure are supplementary, then the lines ‘n’ and ‘m’ are parallel.
However, 110° + 85° = 195°, indicating that 110° and 85° are NOT supplementary.
As a result, the given lines are NOT parallel, according to the Consecutive Interior Angles Theorem.
Example 3: Find the missing angles ∠3, ∠5, and ∠6. In the diagram, ∠4 = 65°.
Solution:
Given: ∠4 = 65°, ∠4 and ∠6 are corresponding angles, therefore;
∠6 = 65°
By supplementary angles theorem, we know;
∠5 + ∠6 = 180°
∠5 = 180° – ∠6 = 180° – 65° = 115°
Since,
∠3 = ∠6
Therefore, ∠3 = 115°.
Consecutive Interior Angles
Consecutive Interior Angles are situated on the same sides of the transversal and in the case of parallel lines, consecutive interior angles add up to 180°, which implies the supplementary nature of Consecutive Interior Angles.
This article explores, almost all the possibilities related to Consecutive Interior Angles which are also called co-interior angles. This article covers a detailed expiation about Consecutive Interior Angles including, its definition, other angles related to transversal, and theorems related to Consecutive Interior Angles as well.
Table of Content
- What are Consecutive Interior Angles?
- Consecutive Interior Angles Definition
- Consecutive Interior Angles Example
- Consecutive Interior Angles for Parallel Lines
- Properties of Consecutive Interior Angles
- Consecutive Interior Angle Theorem
- Converse of Consecutive Interior Angle Theorem
- Consecutive Interior Angles of a Parallelogram
- Consecutive Interior Angles – FAQs
- Define Consecutive Interior Angles.