Question

ABCD is a trapezium in which angle A is equal to X + 45 degree angle b is equal to angle C is equal to 75 degree and Angle d is equal to 2 x minus 15 degree find the value of x and y

Answer 1

Answer:

x = 60°

Step-by-step explanation:

angle sum property in trapezium = 360°

∠A + ∠B + ∠C + ∠D = 360°

(x + 45)° + 75° + 75° + (2x - 15)° = 360°

x + 2x + 45° + 150° - 15° = 360°

3x + 180° = 360°

3x = 360° - 180°

3x = 180°

x = 180°/3

x = 60°

∠A = x + 45°

60° + 45° = 105°

∠D = 2x - 15°

120° - 15° = 105°

∠A = ∠D and ∠B = ∠C

So, trapezium-ABCD is an isosceles trapezium as adjacent angles of the parallel sides are equal