How to find the angle of a sector

Practice Questions

ISEE Upper Level (grades 9-12) Quantitative Reasoning › How to find the angle of a sector

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1

$\bigtriangleup ABC$ is inscribed in a circle. $\overarc {ABC }$ is a semicircle. $m \angle A = 40 ^{\circ }$ .

Which is the greater quantity?

(a) $m \overarc {BAC}$

(b) $m \overarc {BCA }$

2

Circlesectorgeneral9

The arc-length for the shaded sector is . What is the value of , rounded to the nearest hundredth?

3

Icecreamcone 3

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

(a) The area of $\bigtriangleup ABC$

(b) The area of the orange semicircle

4

Inscribed angle 4

Figure NOT drawn to scale

In the above diagram, $m \overarc {BC } = 100^{\circ }$ .

Which is the greater quantity?

(a) $m \angle A$

(b) $m \angle B$

5

Tangents 1

Figure NOT drawn to scale.

Refer to the above diagram. $m \overarc {NO}$ is the arithmetic mean of $m \overarc {NP}$ and $m \overarc {OP}$ .

Which is the greater quantity?

(a) $m \angle NTO$

(b) $60 ^{\circ }$

6

Circle 2

In the above figure, $\overline{AD}$ is a diameter of the circle. Which is the greater quantity?

(a) $m \angle ADB$

(b) $m \angle ACB$

7

Inscribed angle 2

In the above figure, $\overline{AD}$ is a diameter of the circle.

Which is the greater quantity?

(a) $m \angle CAD$

(b) $m \angle CBD$

8

Inscribed angle 3

In the above figure, is the center of the circle, and $m \overarc {AD} = 60 ^{\circ }$ . Which is the greater quantity?

(a)

(b)

9

Circle

Note: Figure NOT drawn to scale

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

(a)

(b) 90

10

Inscribed angle 4

Figure NOT drawn to scale

In the above diagram, $BA = AX \sqrt{2}$ .

Which is the greater quantity?

(a) $m \overarc{AD}$

(b) $m \overarc{BC}$

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