Chapter 6, Problem 8CR

Solution

To calculate: The measure of $\angle 1$

The measure of $\angle 1$ is ${40}^{\circ }$

Given information: The measures of two angles are given i.e., ${140}^{\circ }$ and ${70}^{\circ }$ is provided in the question which will help to find the solution.

Concept used: The concept of linear angle theorem has been used here.

Calculation: Let the two angles be $\angle 1$ and $\angle 2$

Now, $\angle 2+{140}^{\circ }={180}^{\circ }$ (linear angle)

➔ $\angle 2={40}^{\circ }$

And, $\angle 3+{70}^{\circ }={180}^{\circ }$ (linear angle)

➔ $\angle 3={110}^{\circ }$

And, $\angle 1=\angle 2$ (alternate angle property)

Conclusion: Hence, the measure of $\angle 1$ is ${40}^{\circ }$