How to find the angle for a percentage of a circle

Math · Learn by Concept

Help Questions

Math › How to find the angle for a percentage of a circle

1 - 2

1

Arcs

$m \angle AXC = 135^{\circ }$ ; $arc\ \widehat{AB} = 24^{\circ }$ ; $arc\ \widehat{AC} = 94^{\circ }$

Find the degree measure of $arc\ \widehat{CD}$ .

$66^{\circ }$

CORRECT

Not enough information is given to answer this question.

0

$164^{\circ}$

0

$82^{\circ}$

0

$132^{\circ }$

0

Explanation

When two chords of a circle intersect, the measure of the angle they form is half the sum of the measures of the arcs they intercept. Therefore,

$m \angle AXB = \frac{m; \widehat{AB} + m; \widehat{CD} }{2}$

Since $\angle AXB$ and $\angle AXC$ form a linear pair, $m \angle AXB + m \angle AXC = 180$ , and $m \angle AXB = 180 - m \angle AXC = 180 - 135 = 45^{\circ }$ .

Substitute $m; \widehat{AB} = 24$ and $m \angle AXB = 45$ into the first equation:

$45 = \frac{24 + m; \widehat{CD} }{2}$

$90 =24 + m; \widehat{CD}$

$66 = m; \widehat{CD}$

2

A sector comprises 20% of a circle. What is the central angle of the sector?

CORRECT

0

0

0

Explanation

Proporations can be used to solve for the central angle. Let equal the angle of the sector.

$\frac{20}{100}=\frac{x}{360}$

Cross mulitply:

Solve for :

$\frac{7200}{100}=\frac{100x}{100}$

Return to subject

AI Study CoachYour personal study buddy

Instant TutoringConnect with a tutor now

Request a TutorGet matched with an expert

Live ClassesJoin interactive classes

Questions of the DayDaily practice to build your skills

FlashcardsStudy and memorize key concepts

WorksheetsBuild custom practice quizzes

AI SolverStep-by-step problem solutions

Learn by ConceptMaster concepts step by step

Diagnostic TestsAssess your knowledge level

Practice TestsTest your skills with exam questions

GamesLearn through free games