DSQ: Calculating an angle in a quadrilateral

Practice Questions

GMAT Quantitative Reasoning › DSQ: Calculating an angle in a quadrilateral

Questions

10

1

True or false: Quadrilateral is a rectangle.

Statement 1: $\bigtriangleup QUA \cong \bigtriangleup ADQ$

Statement 2: $\bigtriangleup QUA \cong \bigtriangleup UQD$

2

Given Parallelogram .

True or false: $\overline{AC} \perp \overline{BD}$

Statement 1:

Statement 2: $m \angle ABC = 45^{\circ }$

3

Quadrilateral is inscribed in a circle.

What is $m \angle Q$ ?

Statement 1: $m \angle A = 140 ^{\circ }$

Statement 2: $m \widehat{UAD} = 80 ^{\circ }$

4

Rectangle

The above shows Parallelogram . Is it a rectangle?

Statement 1: $m \angle 1 = 90 ^{\circ }$

Statement 2: $(AB)^{2} + (BC)^{2} = (AC)^{2}$

5

True or false: Quadrilateral is a rectangle.

Statement 1: $\angle Q$ and $\angle A$ are right angles.

Statement 2: $\overline{QU} \cong \overline{AD}$

6

Rectangle

Refer to the above figure. You are given that Polygon is a parallelogram but not that it is a rectangle. Is it a rectangle?

Statement 1: $\angle BAD \cong \angle 1$

Statement 2: $\angle DAC$ and $\angle DCA$ are complementary angles.

7

Are the diagonals of Quadrilateral perpendicular?

(a)

(b)

8

Is parallelogram a rectangle?

Statement 1: $\angle A = 90^{\circ }$

Statement 2:

9

Given a quadrilateral , can a circle be circumscribed about it?

Statement 1: Quadrilateral is an isosceles trapezoid.

Statement 2: $m\angle Q = 120^{\circ }, m \angle A = 60^{\circ }$

10

Given a quadrilateral , can a circle be circumscribed about it?

Statement 1: Quadrilateral is not a rectangle.

Statement 2: $m\angle Q = 120^{\circ }, m \angle A = 50^{\circ }$

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