Calculating an angle in an acute / obtuse triangle

Practice Questions

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

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Two angles of an isosceles triangle measure $(x + 20) ^{\circ}$ and $\left ( 100-x\right )^{ \circ}$ . What are the possible values of ?

$\angle 1$ , $\angle 2$ , and $\angle 3$ are all exterior angles of $\bigtriangleup ABC$ with vertices , , and , respectively.

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

Statement 1: $\angle 1$ , $\angle 2$ , and $\angle 3$ are all obtuse angles.

Statement 2: $\angle A \cong \angle B$ .

Note: For purposes of this problem, $\angle A$ , $\angle B$ , and $\angle C$ will refer to the interior angles of the triangle at these vertices.

Which of the following cannot be the measure of a base angle of an isosceles triangle?

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

Statement 1: $m \angle A + m \angle B < 90 ^{\circ }$

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

$\Delta ABC \sim \Delta XYZ$

$m \angle A = 20 ^{\circ }; m \angle Y = 120 ^{\circ }$

Which of the following is true of $\Delta ABC$ ?

Which of the following is true of a triangle with three angles whose measures have an arithmetic mean of $90^{\circ }$ ?

The measures of the angles of one triangle, in degrees, are .

The measures of the angles of a second triangle, in degrees, are .

What is ?

Two angles of a triangle measure $47 ^{\circ }$ and $23^{\circ }$ . What is the measure of the third angle?

An exterior angle of $\Delta ABC$ with vertex measures $150^{\circ }$ ; an exterior angle of $\Delta ABC$ with vertex measures $110^{\circ }$ . Which is the following is true of $\Delta ABC$ ?

The interior angles of a triangle have measures $x^{\circ }$ , $y^{\circ }$ , and $2x^{\circ }$ . Also,

Which of the following is closest to ?

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