Question

Find measure of central angle of the sector whose perimeter is 25 cm and radius of the circle is 7 cm?

Answer 1

perimeter of sector js
theta*pi*r=25
now r=7
so
theta is 25/22 radian

Answer 2

Answer:

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

$P=l+2r$

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

P=25 cm , r=7 cm

$25=l+2(7)$

$25=l+14$

$l=25-14$

$l=11$

So, The length of the arc is 11 cm.

Angle subtended by a circle is 360 degrees

Circumference of circle is given by,

$C=2\pi r\\C=2\times \frac{22}{7}\times 7\\\\C=44cm$

Angle subtended by arc is given by,

$\theta = 360\times \frac{l}{C}$

$\theta = 360\times \frac{11}{44}$

$\theta =\frac{360}{4}$

$\theta =90^\circ$

Therefore, The measure of central angle is 90 degrees.