7.** **The angles of a quadrilateral are in the ratio 2 : 3
: 5 : 8. Find them in degree as well as in radians.
**Solution **
Let the angles be 2k, 3k, 5k and 8k in degrees.
For a quadrilateral, 2k + 3k + 5k + 8k = 360^{0}
\ 18k = 360^{0} \
k = 20^{0}
\ The angles are 2k = 40^{0}
, 3k = 60^{0} , 5k = 100^{0}
and 8k = 160^{0}
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.
**Solution **
Let the angles of a triangle in A.P. be,
a - d, a and a + d respectively
\ (a - d) + a + (a + d) = 180^{0}
\ 3a = 180^{0}\
a = 60^{0}
\ 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 = 40^{0}
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.
**Solution **
Given that s = 7cm , r = 4 cm with usual notations.
Now we have s = r q^{c} \
q =
= 7 cm = 1.75 rad
10. If D, G, C are respectively the numbers in degrees, grades
and radians of an angle. Show that
(i)
(ii)
Solution
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