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The adjacent angles of a parallelogram are (2x - 4)° and (3x - 1)°. Find the measures of all angles of the parallelogram.

Solution:

Given, the two adjacent angles of a parallelogram are (2x - 4)° and (3x - 1)°

We have to find the measures of all these angles.

We know that the sum of adjacent angles of a parallelogram are supplementary.

So, (2x - 4)° + (3x - 1)° = 180°

2x - 4° + 3x - 1° = 180°

5x - 5° = 180°

5x = 180° + 5°

5x = 185°

x = 185°/5

x = 37°

Now, 2x - 4 = 5(37°) - 4° = 74° - 4° = 70°

3x - 1° = 3(37°) - 1° = 111° - 1° = 110°

We know that the opposite angles are equal in a parallelogram.

Therefore, the required angles are 70°, 110°, 70° and 110°.

✦ Try This: If two adjacent angles of a parallelogram are (x - 1)° and (3x + 6)°, then find the measures of these angles.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 138

Summary:

The adjacent angles of a parallelogram are (2x - 4)° and (3x - 1)°. The measures of all angles of the parallelogram are 70°, 110°, 70° and 110°.

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