Q3 of 9 Page 150

If one angle of a parallelogram is 36° less than the twice its adjacent angles, then find the angles of the parallelogram.

Sum of adjacent angles of parallelogram = 180°


Given:


One angle of Parallelogram = 2 (adjacent angle) – 36°


Let the angle of parallelogram be x



Sum of adjacent angles of parallelogram = 180°



2x +x + 36° = 180°


3x = 180° – 36°


3x = 144°



x = 48°



Now from the diagram, we know that,


∠A = 48°


∠B = 180° – 48° = 132°


∠C = ∠A = 48°


∠D = ∠B = 132°


More from this chapter

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1

Find the area of quadrilateral ABCD in which AB = 7 cm, BC = 6 cm, CD = 12 cm, DA = 15 cm, and AC = 9 cm.

 2

In a quadrilateral ABCD, AO and BO are the bisectors of angle A and angle B. Prove that .

 4

A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is

(A) 55°


(B) 50°


(C) 40°


(D) 25°

 5

In a cyclic quadrilateral ABCD. ∠A= (2x+4)°, ∠B = (y+3)°, ∠C = (2y+10)°, and ∠D = (4x–5)°. Find the measure of each angle.