How to find an angle in an acute / obtuse triangle

Practice Questions

SSAT Upper Level Quantitative (Math) › How to find an angle in an acute / obtuse triangle

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Find the angle measurement of .

The interior angles of a triangle measure $x^{\circ } , \left ( x+ 26\right )^{\circ } , \left (2x+ 1\right )^{\circ }$ . Of these three degree measures, give the greatest.

If the vertex angle of an isoceles triangle is $64^{\circ}$ , what is the value of one of its base angles?

Triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram.

$45^{\circ } \leq m \angle 1 \leq 50^{\circ }$

$60^{\circ } \leq m \angle 2 \leq 70 ^{\circ }$

Which of the following could be a measure of $\angle 3$ ?

$\bigtriangleup ABC$ is a right triangle with right angle $\angle A$ . is located on $\overline{AB}$ so that, when $\overline{CD}$ is constructed, isosceles triangles $\bigtriangleup ADC$ and $\bigtriangleup BDC$ are formed.

What is the measure of $\angle B$ ?

An isosceles triangle has an angle whose measure is $70^{\circ }$ .

What could be the measures of one of its other angles?

(a) $40^{\circ }$

(b) $55^{\circ }$

One of the interior angles of a scalene triangle measures $54^{\circ }$ . Which of the following could be the measure of another of its interior angles?

Given: $\bigtriangleup ABC$ with $m \angle A = 20^{\circ }, m \angle B = 32^{\circ }$ . Locate on $\overline{AB}$ so that $\overrightarrow{CD}$ is the angle bisector of $\angle ACB$ . What is $m \angle CDB$ ?

Given: $\bigtriangleup ABC$ with $m \angle B = 74^{\circ }$ . is located on $\overline{AB}$ so that $\overrightarrow{CD}$ bisects $\angleACB$ $\angle ACB$ and forms isosceles triangle $\bigtriangleup BCD$ .

Give the measure of $\angle A$ .

Triangle_a

Figure NOT drawn to scale.

If $x = 72^{\circ }$ and $y = 43^{\circ }$ , evaluate .

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