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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掳and 80掳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掳and x are alternate interior angles. Therefore, they are equal, that is, x=30掳.

03

Step 3. Apply an angle sum theorem.

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

04

Step 4. Description of step.

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

=180鈭�50鈭�30=100掳

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掳and y are supplementary angles. Therefore,

100+y=180y=180鈭�100=80

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

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In pentagon PQRST,m鈭�P=60 and m鈭�Q=130.鈭�S and鈭�T are each three times as large as 鈭�R.

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If two lines are cut by a transversal and same-side interior angles are complementary, then the lines are ?炉 parallel.

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