How to find an angle

Practice Questions

ISEE Upper Level (grades 9-12) Quantitative Reasoning › How to find an angle

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1

A hexagon has six angles with measures $(x-5)^{\circ}, x^{\circ}, (x+5)^{\circ}, (y-10)^{\circ}, y^{\circ}, (y + 10)^{\circ}.$

Which quantity is greater?

(a)

(b) 240

2

Which is the greater quantity?

(a) The sum of the measures of the exterior angles of a thirty-sided polygon, one per vertex

(b) The sum of the measures of the exterior angles of a forty-sided polygon, one per vertex

3

Given Trapezoid , where $\overline{TR} \parallel \overline{PA}$ . Also, $m \angle A > m\angle P$

Which is the greater quantity?

(a) $m\angle T$

(b) $m \angle R$

4

Trapezoid

The above diagram depicts trapezoid . Which is the greater quantity?

(a) $m \angle T + m \angle P$

(b) $m \angle R + m \angle A$

5

In a certain quadrilateral, three of the angles are $65^{\circ}$ , $120^{\circ}$ , and $34^{\circ}$ . What is the measure of the fourth angle?

6

Right_triangle

Note: Figure NOT drawn to scale.

Refer to the above figure. Which is the greater quantity?

(a)

(b)

7

Right triangle $\Delta ABC$ has right angle $\angle B$ .

$m\angle A = \left ( x + 30 \right )^ {\circ} ,m\angle C = \left ( 2x- 57\right ) ^ {\circ}$

Which is the greater quantity?

(a) $m\angle A$

(b) $m\angle C$

8

Let the three angles of a triangle measure , , and .

Which of the following expressions is equal to ?

9

$\angle 1$ and $\angle 2$ are complementary; $m \angle 1 =2 m \angle 2 - 50$ .

Which is the greater quantity?

(A) $m \angle 1$

(B) $m \angle 2$

10

You are given pentagon .

$\angle A \cong \angle B \cong \angle C$

$\angle D \cong \angle E$

Which is the greater quantity?

(A) $108 ^{\circ }$

(B) $m\angle D$

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