Question

163. Find measure of central angle of the sector
whose perimeter is 25 cm and radius of the
circle is 7 cm?
A. 450
B. 22.5°
C. 135°
D. 90°
with explain​

Answer 1

The measure of central angle is 90 degrees.

Step-by-step explanation:

Given : Sector perimeter is 25 cm and radius of the circle is 7 cm.

To find : Measure of central angle of the sector?

Solution :

We know, The perimeter of sector is defined as

P=l+2rP=l+2r

where, l is the length arc and r is the radius.

P=25 cm , r=7 cm

25=l+2(7)25=l+2(7)

25=l+1425=l+14

l=25-14l=25−14

l=11l=11

So, The length of the arc is 11 cm.

Angle subtended by a circle is 360 degrees

Circumference of circle is given by,

\begin{gathered}C=2\pi r\\C=2\times \frac{22}{7}\times 7\\\\C=44cm\end{gathered}

C=2πr

C=2×

7

22

×7

C=44cm

Angle subtended by arc is given by,

\theta = 360\times \frac{l}{C}θ=360×

C

l

\theta = 360\times \frac{11}{44}θ=360×

44

11

\theta =\frac{360}{4}θ=

4

360

\theta =90^\circθ=90

∘

Therefore, The measure of central angle is 90 degrees.