Unit 7, Lesson 16

Radian Sense

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Integrated Math 2

Practice

Problem 1

Student Task Statement

Match each diagram showing a sector with the measure of its central angle in radians.

<p>Circles A through F with sectors shown.</p>

diagram A

diagram B

diagram C

diagram D

diagram E

diagram F

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Problem 2

Student Task Statement

In the circle, sketch a central angle that measures radians.

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Problem 3

Student Task Statement

Angle has a measure of radians. The length of arc is units, and the radius is 12 units. What is the area of sector ?

<p><strong>Angle A O C. Point B falls on perimeter, between points A and C. A B labeled 2 pi. A O labeled 12. Sector B O C shaded.</strong></p>

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Problem 4

ForLesson 15: A New Way to Measure Angles

Student Task Statement

Calculate the radian measure of a 30-degree angle. Use any method you like, including sketching in the circle diagram provided. Explain or show your reasoning.

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Problem 5

ForLesson 15: A New Way to Measure Angles

Student Task Statement

Lin thinks that the central angle in Circle A is congruent to the central angle in Circle B. Do you agree with Lin? Show or explain your reasoning.

<p>Circle with sector with central angle. Radius 12. Arc measure 4 pi.</p> — Circle A

<p>Circle with radius = 3. Sector with length = pi.</p> — Circle B

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Problem 6

ForLesson 14: Angles, Arcs, and Radii

Student Task Statement

<p>Circle radius of 5 units. A 60 degree sector is noted.</p> — Circle A

<p>A circle, radius 9 units. A 90 degree sector is noted.</p> — Circle B

Select all true statements.

The sector in Circle B has a larger area than the sector in Circle A.
Not taking into account the sectors, Circle A and Circle B are similar.
The fraction of the circumference taken up by the arc outlining the sector in Circle A is smaller than the fraction of the circumference taken up by the arc outlining the sector in Circle B.
The ratio of the area of Circle A’s sector to its total area is .

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Problem 7

ForLesson 13: Part to Whole

Student Task Statement

Match each arc length and radius with the measure of the central angle that defines the arc.

arc length cm, radius 5 cm
arc length cm, radius 10 cm
arc length cm, radius 12 cm
arc length cm, radius 18 cm

angle: 30 degrees
angle: 72 degrees
angle: 135 degrees
angle: 180 degrees

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Problem 8

ForLesson 8: Quadrilaterals in Circles

Student Task Statement

Quadrilateral is shown with the given angle measures. Select all true statements.

<p>Quadrilateral A B C D inscribed in a circle. Angle A B C is 125 degrees, angle B C D is 40 degrees.</p>

Angle measures 140 degrees.
The measures of angle and angle must add to 180 degrees.

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The ratio of Circle A’s area to Circle B’s area is .

Angle measures 55 degrees.

Angle measures 40 degrees.

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Radian Sense

Practice

Problem 1

Student Task Statement

Problem 2

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Problem 3

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Problem 4

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Problem 5

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Problem 6

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Problem 7

Student Task Statement

Problem 8

Student Task Statement

Lesson 16 Resources