The trapezium is an isosceles trapezium. Then the measure of all angles will be 54°, 36°, 36°, and 54°.
It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.
In the adjoining figure, ABCD is an isosceles trapezium in which angle ∠BCD = 2x and angle ∠ABC = 3x.
Then all the angles of the trapezium will be
Agngle ∠BCD = ∠ADC and angle ∠ABC = ∠BAD because the trapezium is an isosceles trapezium. Then we have
Then the value of x will be
∠ABC + ∠BCD + ∠CDA + ∠DAB = 180°
3x + 2x + 2x + 3x = 180°
10x = 180°
x = 18°
Then the measure of all angles will be
∠ABC = ∠BAD = 3x = 3 × 18 = 54°
∠BCD = ∠ADC = 2x = 2 × 18 = 36°
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