7. The angles of a quadrilateral are in the ratio 2 : 3
: 5 : 8. Find them in degree as well as in radians.
Let the angles be 2k, 3k, 5k and 8k in degrees.
For a quadrilateral, 2k + 3k + 5k + 8k = 3600
\ 18k = 3600 \
k = 200
\ The angles are 2k = 400
, 3k = 600 , 5k = 1000
and 8k = 1600
8. The angles of a triangle are in A.P. such that the greatest
is five times the least. Find the angles in degrees and radians.
Let the angles of a triangle in A.P. be,
a - d, a and a + d respectively
\ (a - d) + a + (a + d) = 1800
\ 3a = 1800\
a = 600
\ The greatest angle be (60 +d)0
and the least angle be
(60 - d)0
Given that (60 + d) = 5 (60 - d)
\ 60 + d = 300 - 5d
\ 6d = 240 \
d = 400
9. The length of an arc of a circle is 7 cm. Find the angle (in
degrees and radians) it makes at the centre, if the radius is 4
cm. Give the answer to three significant digit.
Given that s = 7cm , r = 4 cm with usual notations.
Now we have s = r qc \
= 7 cm = 1.75 rad
10. If D, G, C are respectively the numbers in degrees, grades
and radians of an angle. Show that