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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

The lengthsRS Aggarwal & V Aggarwal - Mathematics

In each of RS Aggarwal & V Aggarwal - Mathematics

If the bisectors RD Sharma - Mathematics

In Fig. 14.113, PRD Sharma - Mathematics

In Fig. 14.114, ARD Sharma - Mathematics

Each side oRS Aggarwal & V Aggarwal - Mathematics

If ABCD is a rhomRD Sharma - Mathematics

If ABCD is a rectRD Sharma - Mathematics