Question 1: Two opposite angles of a parallelogram are (3x – 2)0 and (50 – x) 0. Find the measure of each angle of the parallelogram.
Solution:
Given: Two opposite angles of a parallelogram are (3x – 2)0 and (50 – x) 0.
We know, opposite angles of a parallelogram are equal.
(3x – 2)0 = (50 – x) 0
3x + x = 50 + 2
4x = 52
x = 13
Value of x is = 130
Therefore,
(3x-2) 0 = (3(13) – 2) = 370
(50-x) 0 = (50 – 13) = 370
Adjacent angles of a parallelogram are supplementary.
x + 37 = 1800
x = 1800 − 370 = 1430
Therefore, required angles are : 370, 1430, 370 and 1430.
Question 2: The perimeter of a parallelogram is 22 cm. If the longer side measure 7.5 cm, what is the measure of shorter side?
Solution:
Perimeter of a parallelogram = 22 cm. (Given)
Longer side = 7.5 cm
Let x be the shorter side.
Perimeter = 2x + 2×7.5
22 = 2x + 15
2x = 22 – 13 = 7
or x = 3.5
Measure of shorter side is 3.5 cm.
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