ANGLES OF A CIRCLE LESSON 1 2 MATH

Arc • A piece of a circle Semicircle • An arc formed by the

Semicircle • An arc formed by the diameter of the circle. It splits the

Minor arc • An arc that is less than a semicircle Major arc •

Use the diagram to below to name: 1. Two semicircles 2. A minor arc

The measure of a minor arc is equal to the measure of its central

Find the measure of… Arc PR Arc RS Arc PS

Inscribed angle • An angle whose vertex is located on the edge of the

Find the measure of the arc or angle in blue.

If two inscribed angles intersect the same arc, then the angles are congruent 60

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

The measure of an angle formed by a chord and a tangent is equal

An angle inscribed in a semicircle is a right angle.

Find the values of x, y, and z in the circle below. xo yo

State the indicated degree measure. 70 o 1. Arc VW 2. Angle W 3.

The measure of an angle formed by two chords that intersect inside a circle,

The measure of an angle formed by two secants, two tangents, or a tangent

Find the measure of 1 and 2. 70 o 1 50 o 26 o

Use the figure to find the measure of the following. 1. Arc WT 2.

Given: AB is a tangent, AF is a diameter, arc AG = 100, Arc

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ANGLES OF A CIRCLE LESSON 1 – 2 MATH III

Arc • A piece of a circle Semicircle • An arc formed by the diameter of the circle. It splits the circle into two congruent halves.

Semicircle • An arc formed by the diameter of the circle. It splits the circle into two congruent halves. Two semicircles are and

Minor arc • An arc that is less than a semicircle Major arc • An arc that is more than a semicircle Central angle • An angle in which the vertex is the center of the circle

Use the diagram to below to name: 1. Two semicircles 2. A minor arc 3. Two major arcs 4. An acute central angle 5. An obtuse central angle 6. Two congruent arcs

The measure of a minor arc is equal to the measure of its central angle. 70 o The measure of central angle MOP = 70 o The measure of arc MP = 70 o.

Find the measure of… Arc PR Arc RS Arc PS

Arc Measure Addition

Inscribed angle • An angle whose vertex is located on the edge of the circle 40 o 80 o The measure of an inscribed angle is equal to half the measure of its intercepted arc.

Find the measure of the arc or angle in blue.

If two inscribed angles intersect the same arc, then the angles are congruent 60 o 120 o

What is the measure of Angle F?

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.

An angle inscribed in a semicircle is a right angle.

Find the values of x, y, and z in the circle below. xo yo 55 o zo

State the indicated degree measure. 70 o 1. Arc VW 2. Angle W 3. Arc VX 4. Angle WVX 5. Arc XW

The measure of an angle formed by two chords that intersect inside a circle, is equal to half the sum of the measures of the two intercepted arcs. 1

Find the measure of Angle x.

The measure of an angle formed by two secants, two tangents, or a tangent and a secant drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs Two secants Tangent and Secant Two tangents

Find the measure of Angle x.

Find the measure of 1 and 2. 70 o 1 50 o 26 o 2

Use the figure to find the measure of the following. 1. Arc WT 2. TVS 3. RVS 4. Arc RS 110 o 30 o 100 o

Given: AB is a tangent, AF is a diameter, arc AG = 100, Arc CE = 30, Arc EF = 25. 6 8 3 7 2 1 Find 1, 2, 3, 4, 5, 6, 7, 8 5 4