Question

The angles A, B, C and D of a quadrilateral ABCD have measures in the ratio 2 : 4 : 5 : 7. Find the measures of these angles. What type of quadrilateral is it? Give reasons. [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks



Let the measures of the angles be 2x, 4x, 5x and 7x

$\Rightarrow 2x+4x+5x+7x={360}^{\circ }$

$\Rightarrow 18x={360}^{\circ }\Rightarrow x={20}^{\circ }$

$\Rightarrow \angle A={40}^{\circ },\angle B={80}^{\circ },\angle C={100}^{\circ },\angle D={140}^{\circ }$

As $\angle A+\angle D={180}^{\circ }$ and $\angle B+\angle C={180}^{\circ }$

$\Rightarrow CD\parallel AB\Rightarrow ABCD$ is a trapezium.