Question

NO LINKS!! URGENT HELP PLEASE!!

Please help with 36​

Answer 1

Explanation:

Let the centre be C.

Since TR is a straight line,

∠SCT + ∠SCR = 180

∠SCT = 180 - 53

∠SCT = 127

The angle of a semicircle is 180°. Minor arcs are arcs less than a semicircle i.e. less than 180° and major arcs are arcs greator than a semicircle i.e. greater than 180°.

a) arc(SPT) has measure of 90 + 65 + 25 + 53 = 233° > 180° and hence a major arc

Also 1° = π/180 radians

233° = 233 * π/180 = 1.29π radians

b) arc(ST) has measure of 127° < 180° and hence a minor arc

127° = 127 * π/180 = 0.71π radians

c) arc(RST) has a measure of 53 + 127 = 180° which is a semicircle

180° = 180* π/180 = π radians

d) arc(SP) has a measure of 53 + 25 + 65 = 143° < 180° and hence a minor arc

143° = 143* π/180 = 0.79π radians

e) arc(QST) has a measure of 25 + 53 + 127 = 205° > 180° and hence a major arc

205° = 205 * π/180 = 1.14π radians

f) arc(TQ) has a measure of 90 + 65 = 155° < 180° and hence a minor arc

155° = 155 * π/180 = 0.86π radians

Answer 2

`\text{a.} \quad \text{Major arc}:\;\;\overset{\frown}{SPT}=233^(\circ)`

`\text{b.} \quad \text{Minor arc}:\;\;\overset{\frown}{ST}=127^(\circ)`

`\text{c.} \quad \text{Semicircle}:\;\;\overset{\frown}{RST}=180^(\circ)`

`\text{d.} \quad \text{Minor arc}:\;\;\overset{\frown}{SP}=143^(\circ)`

`\text{e.} \quad \text{Major arc}:\;\;\overset{\frown}{QST}=205^(\circ)`

`\text{F.} \quad \text{Minor arc}:\;\;\overset{\frown}{TQ}=155^(\circ)`

Explanation:

Major Arc

A major arc is an arc in a circle that measures more than 180°.

It is named with three letters: two endpoints and a third point on the arc.

Minor Arc

A minor arc is an arc in a circle that measures less than 180°.

It is named with two letters: its two endpoints.

Semicircle

A semicircle is a special case of an arc that measures exactly 180°.

The endpoints of the semicircle are located on the diameter, and the semicircle divides the circle into two equal parts.

Arc of a circle

The measure of an arc of a circle is equal to the measure of its corresponding central angle.

`\hrulefill`

a) Arc SPT is a major arc since it is named with three letters.

It begins at point S, passes through point P, and ends at point T.

`\begin{aligned}\overset{\frown}{SPT}&=\overset{\frown}{SR}+\overset{\frown}{RQ}+\overset{\frown}{QP}+\overset{\frown}{PT}\\&=53^(\circ)+25^(\circ)+65^(\circ)+90^(\circ)\\&=233^(\circ)\end{aligned}`

`\hrulefill`

b) Arc ST is a minor arc since it is named with two letters.

It is measured in a counterclockwise direction from point S to point T.

`\begin{aligned}\overset{\frown}{ST}&=360^(\circ)-\overset{\frown}{SPT}\\&=360^(\circ)-233^(\circ)\\&=127^(\circ)\end{aligned}`

`\hrulefill`

c) Arc RST is a semicircle.

Arc RST is a semicircle since its endpoints are located on the diameter of the circle, RT.

`\overset{\frown}{RST}=180^(\circ)`

`\hrulefill`

d) Arc SP is a minor arc since it is named with two letters.

It is measured in a clockwise direction from point S to point P.

(If it was measured in a counterclockwise direction, it would be a major arc, as it would be more than 180°, and therefore would be named using three letters).

`\begin{aligned}\overset{\frown}{SP}&=\overset{\frown}{SR}+\overset{\frown}{RQ}+\overset{\frown}{QP}\\&=53^(\circ)+25^(\circ)+65^(\circ)\\&=143^(\circ)\end{aligned}`

`\hrulefill`

e) Arc QST is a major arc since it is named with three letters.

It begins at point Q, passes through point S, and ends at point T.

`\begin{aligned}\overset{\frown}{QST}&=\overset{\frown}{QR}+\overset{\frown}{RS}+\overset{\frown}{ST}\\&=25^(\circ)+53^(\circ)+127^(\circ)\\&=205^(\circ)\end{aligned}`

`\hrulefill`

f) Arc TQ is a minor arc since it is named with two letters.

It is measured in a counterclockwise direction from point T to point Q.

(If it was measured in a clockwise direction, it would be a major arc, as it would be more than 180°, and therefore would be named using three letters).

`\begin{aligned}\overset{\frown}{TQ}&=\overset{\frown}{TP}+\overset{\frown}{PQ}\\&=90^(\circ)+65^(\circ)\\&=155^(\circ)\end{aligned}`