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Chapter 3: Q11 (page 97)

Find the values of x andy.

Short Answer

Expert verified

The values of x and y are 30°and 80°respectively.

Step by step solution

01

Step 1. Observe the given figure and highlight angle x and angle y.

02

Step 2. Description of step.

From the figure, it can be observed that the two angles, 30°and x are alternate interior angles. Therefore, they are equal, that is, x=30°.

03

Step 3. Apply an angle sum theorem.

The sum of measures of all interior angles of a triangle is 180°.

04

Step 4. Description of step.

From the given figure, it can be observed that angles, 50°,30°and unknown angle are interior angles of a triangle. Therefore, the measure of unknown angles is

=180−50−30=100°

05

Step 5. Apply the definition of supplementary angles.

If the sum of measure of two angles is then they are said to be supplementary angles.

06

Step 6. Description of step.

From the given figure, it can be observed that angles, 100°and y are supplementary angles. Therefore,

100+y=180y=180−100=80

Therefore, the values of x and y are 30°and 80° respectively.

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