Solution: Given that the adjacent angles of a parallelogram are in the ratio 3:2. Thus, the angles are 3x and 2x respectively. We know that the sum of the measures of adjacent angles is 180° for a parallelogram. ∠A + ∠B = 180° 3x + 2x = 180° 5x = 180° x = 180°/5 x = 36° Thus, one of the angles = 3x 3(36°) = 108° The other angle is 2x 2(36°) = 72° The other two angles are 72° and 108° since opposite angles of a parallelogram are equal. Thus, the measures of the angles of the parallelogram are 108°, 72°, 108°, and 72° ☛ Check: NCERT Solutions for Class 8 Maths Chapter 3 Video Solution: NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3 Question 5 Summary: The measures of two adjacent angles of a parallelogram are in the ratio 3:2. The measures of each of the angles of the parallelogram are 108°, 72°, 108°, and 72° ☛ Related Questions: Math worksheets and If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are ______.
If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are 72°, 108°. Explanation: Let the angles be 2x, 3x The adjacent angles of a parallelogram are always supplementary and the opposite angles are always equal 2x + 3x = 180° ⇒ 5x = 180° ⇒ x = 36° So, the angles are 2 × 36 = 72° 3 × 36 = 108° Concept: Properties of a Parallelogram - Property: The adjacent angles in a parallelogram are supplementary. Is there an error in this question or solution? > Solution Given, two adjacent angles of a parallelogram are in the ratio 2 : 3 Let the angles be 2x and 3x. Then, 2x+3x=180∘ [∵ adjacent angles of a parallelogram are supplementary] ⇒5x=180∘⇒x=36∘ Hence, the measures of the angles are 2x=2×36∘=72∘ and 3x=3×36∘=108∘. Mathematics NCERT Exemplar Standard VIII Suggest Corrections 5 |