DSQ: Calculating an angle in an acute / obtuse triangle

Practice Questions

GMAT Quantitative Reasoning › DSQ: Calculating an angle in an acute / obtuse triangle

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1

$\angle 1$ is an exterior angle of $\bigtriangleup ABC$ at $\angle A$ .

Is $\bigtriangleup ABC$ an acute triangle, a right triangle, or an obtuse triangle?

Statement 1: $\angle 1$ is an acute angle.

Statement 2: $m \angle B + m \angle C = 80 ^{\circ }$

2

Is $\Delta ABC$ an isosceles triangle?

Statement 1: $m \angle A + m \angle B = 100 ^{\circ }$

Statement 2: $m \angle A + m \angle C = 100 ^{\circ }$

3

Is $\bigtriangleup ABC$ an acute triangle, a right triangle, or an obtuse triangle?

Statement 1:

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

4

Is $\Delta ABC$ an acute, right, or obtuse triangle?

Statement 1: $\angle A$ is complementary to $\angle C$ .

Statement 2: The triangle has exactly two acute angles.

5

Is $\Delta ABC$ an acute, right, or obtuse triangle?

Statement 1: There are exactly two acute angles.

Statement 2: The exterior angles of the triangle at vertex are both acute.

6

A triangle contains a $110^{\circ}$ angle. What are the other angles in the triangle?

(1) The triangle is isosceles.

(2)The triangle has a perimeter of 12.

7

Chords

Note: Figure NOT drawn to scale

Refer to the above figure. Is $\Delta ABC$ an equilateral triangle?

Statement 1: $m \widehat{AB} = 120 ^{\circ }$

Statement 2: $m \widehat{BC} = 140 ^{\circ }$

8

A triangle has an interior angle of measure $30^{\circ }$ . Give the measures of the other two angles.

Statement 1: The triangle is isosceles.

Statement 2: The triangle is obtuse.

9

Triangle_b

Note: figure NOT drawn to scale.

$m \angle A = 46 ^{\circ }$ . What is $m \angle 1$ ?

Statement 1: $\overline{AB} \cong \overline{AC}$

Statement 2: $m \angle B = 67 ^{\circ }$

10

Chords

Note: Figure NOT drawn to scale

Refer to the above figure. Is $\Delta ABC$ an equilateral triangle?

Statement 1: $m \widehat{ABC} = 240 ^{\circ }$

Statement 2: $m \widehat{ACB} = 260 ^{\circ }$

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