Q. 63.7( 12 Votes )

# If angles A, B, C

Answer :

Given: Ratio of angles is 3: 7: 6: 4

Let the angles be 3x, 7x, 6x and 4x.

Sum of all angles of a quadrilateral is 360°

3x + 7x + 6x + 4x = 360°

20x = 360° x = 18°

Now,

Angles of quadrilateral are

A = 3x = 3 × 18° = 54°

B = 7x = 7 × 18° = 126°

C = 6x = 6 × 18° = 108°

D = 4x = 4 × 18° = 72° Extend DC to E

Now,

BCE + BCD = 180° [ sum of angles on a straight line = 180°]

⇒ ∠BCE + BCD = 180°

⇒ ∠BCE + 108° = 180°

⇒ ∠BCE = 180° – 108°

⇒ ∠BCE = 72°

BCE = ADC = 72°

BC AD

Hence, it is a trapezium.

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