The figure shows a circle with center O O O , diameter A C ‾ \overline{AC} A C , and inscribed Δ A C B \Delta ACB Δ A C B . If m ∠ A B C = 90 ° m\angle ABC=90\degree m ∠ A B C = 9 0 ° , m ∠ C = 5 x − 2 m\angle C=5x-2 m ∠ C = 5 x − 2 and m ∠ A = 2 x + 8 m\angle A=2x+8 m ∠ A = 2 x + 8 , what is the m ∠ B A C m\angle BAC m ∠ B A C and m ∠ B C A m\angle BCA m ∠ B C A ?

m ∠ B A C = 32 ° a n d m ∠ B C A = 58 ° m\angle BAC=32\degree\ and\ m\angle BCA=58\degree m ∠ B A C = 3 2 ° a n d m ∠ B C A = 5 8 °

m ∠ B A C = 12 ° a n d m ∠ B C A = 78 ° m\angle BAC=12\degree\ and\ m\angle BCA=78\degree m ∠ B A C = 1 2 ° a n d m ∠ B C A = 7 8 °

m ∠ B A C = 45 ° a n d m ∠ B C A = 45 ° m\angle BAC=45\degree\ and\ m\angle BCA=45\degree m ∠ B A C = 4 5 ° a n d m ∠ B C A = 4 5 °

m ∠ B A C = 30 ° a n d m ∠ B C A = 60 ° m\angle BAC=30\degree\ and\ m\angle BCA=60\degree m ∠ B A C = 3 0 ° a n d m ∠ B C A = 6 0 °

A B C D ABCD A B C D is an inscribed quadrilateral in the circle centered at point O . O. O . Select ALL true statements.

x + z = 180 ° x+z=180\degree x + z = 1 8 0 °

x + 2 y + z + 80 ° = 360 ° x+2y+z+80\degree=360\degree x + 2 y + z + 8 0 ° = 3 6 0 °

y = 50 ° y=50\degree y = 5 0 °

x = 100 ° x=100\degree x = 1 0 0 °

Circles, Angles and Segments

Authored by Corrina Little

Mathematics

7th - 12th Grade

CCSS covered

Used 149+ times

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20 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

An angle is a(n) ______ if the vertex is on a circle and the sides of the angle are chords of the circle.

right angle

acute angle

inscribed angle

intercepted angle

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

A(n) _____ to a circle is a line, ray or segment in the plane of the circle that intersects the circle in exactly one point.

tangent

secant

radius

arc

Tags

CCSS.HSG.C.A.2

CCSS.HSG.C.A.4

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

A ____ is a line, ray, or segment that intersects a circle at two points.

Tangent

Secant

Radius

Arc

Tags

CCSS.HSG.C.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the measure of angle 1?

120

Tags

CCSS.HSG.C.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the measure of angle 2?

125

Tags

CCSS.HSG.C.A.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the value of x?

Tags

CCSS.HSG.C.A.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the value of y?

108

540

Tags

CCSS.HSG.C.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the $m\angle B$ if the measure of arc $AB=120\degree$ and the $m\angle A=42\degree.$

$18\degree$

$60\degree$

$78\degree$

$156\degree$

Tags

CCSS.HSG.C.A.2

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Circles, Angles and Segments

An angle is a(n) ______ if the vertex is on a circle and the sides of the angle are chords of the circle.

A(n) _____ to a circle is a line, ray or segment in the plane of the circle that intersects the circle in exactly one point.