Q138 of 160 Page 144

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

Given, adjacent angles are (2x-4) and (3x-1)

⟹ (2x-4) + (3x-1) = 180

⟹ (5x-5) = 180

⟹ 5(x-1) = 180

⟹ x-1 = 36

⟹ x = 37

⟹ First angle = 2x-4 = (2×37)-4 = 70

⟹ Second angle = 3x-1 = (3×37)-1 = 110

136

PQRS is a rectangle. The perpendicular ST from S on PR divides S in the ratio 2:3. Find TPQ.

137

A photo frame is in the shape of quadrilateral. With one diagonal longer than the other. Is it a rectangle? Why or why not?

139

The point of intersection of diagonals of a quadrilateral divides one diagonal in the ration 1:2. Can it be a parallelogram? Why or why not?

140

The ration between exterior angle and interior angle of a regular polygon is 1:5. Find the number of sides of the polygon.