DSQ: Calculating an angle of a line

Practice Questions

GMAT Quantitative Reasoning › DSQ: Calculating an angle of a line

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1

Lines

Note: Figure NOT drawn to scale.

Refer to the above diagram.

What is the measure of $\angle FCB$ ?

Statement 1: $m \angle FBC = 43 ^{\circ }$

Statement 2: $m \angle DCG = 43 ^{\circ }$

2

What is the measure of $\angle 1$ ?

Statement 1: $\angle 1$ is complementary to an angle that measures $48 ^{\circ }$ .

Statement 2: $\angle 1$ is adjacent to an angle that measures $42 ^{\circ }$ .

3

Lines_3

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate $m \angle 3+ m \angle 4$ .

Statement 1: $m \angle1 + m \angle 5 = 120^{\circ }$

Statement 2: $\bigtriangleup OPQ$ is an equilateral triangle.

4

Lines_3

Note: Figure NOT drawn to scale.

Refer to the above diagram. What is the measure of $\angle 1$ ?

Statement 1: $\bigtriangleup OPQ$ is an equilateral triangle.

Statement 2: $m \angle 3 = 65^{\circ }$

5

Lines_3

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate $m \angle 1+ m \angle 2$ .

Statement 1: $m \angle 2+ m \angle 3 = 122^{\circ }$

Statement 2: $m \angle 3+ m \angle 4 = 126^{\circ }$

6

Lines_3

Note: Figure NOT drawn to scale.

Refer to the above diagram. What is the measure of $\angle 1$ ?

Statement 1: $m \angle 1 = 30 ^{\circ } + 2 \cdot m \angle 2$

Statement 2: $\angle 3$ is a $130 ^{\circ }$ angle.

7

Lines_3

Note: Figure NOT drawn to scale.

Refer to the above diagram. What is the measure of $\angle 1$ ?

Statement 1: $\angle 6$ is a $54 ^{\circ }$ angle.

Statement 2: $\angle 2 \cong \angle 3$

8

Lines_3

Note: Figure NOT drawn to scale.

Refer to the above figure. Evaluate $m \angle 1+ m \angle 2$ .

Statement 1: $m \angle 3 + m \angle 4 + m \angle 5 = 131^{\circ }$

Statement 2: $m \angle 6 + m \angle 7 + m \angle 8 = 131^{\circ }$

9

Lines_4

Note: You may assume that and are not parallel lines, but you may not assume that and are parallel lines unless it is specifically stated.

Refer to the above diagram. Is the sum of the measures of $\angle ADC$ and $\angle DCB$ less than, equal to, or greater than $180^{\circ }$ ?

Statement 1: $m \angle 1 + m \angle 6 = 181^{\circ }$

Statement 2: $m \angle 7 + m \angle 12 = 179^{\circ }$

10

Find the angle made by and the -axis.

I) goes through the origin and the point .

II) makes a degree angle between itself and the -axis.

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