Advertisements
Advertisements
Question
Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)
Advertisements
Solution
Let the angles of triangles be a, a + d, a + 2d
We know that, sum of angles of triangle = 180°
∴ a + a + d + a + 2d = 180°
∴ 3a + 3d = 180°
∴ 3(a + d) = 180°
∴ (a + d) = `(180ϒ)/3`
∴ a + d = 60° ......(i)
According to the given conditions,
Smallest angle, a = 5 × d
∴ a = 5d
Putting the value of an in equation (i)
∴ 5d + d = 60°
∴ 6d = 60°
∴ d = `(60ϒ)/6`
∴ d = 10°
Putting the value of d in (i)
∴ a + d = 60°
∴ a + 10 = 60°
∴ a = 60° – 10
∴ a = 50°
∴ a + 2d = 50° + 2(10)
= 50° + 20
= 70°
∴ Angles of triangle are 50°, 60°, 70° respectively.
APPEARS IN
RELATED QUESTIONS
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 3 + 4n
Also, find the sum of the first 15 terms.
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
Find an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40.
The sum of the first n terms of an AP is `((5n^2)/2 + (3n)/2)`. Find the nth term and the 20th term of this AP.
The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹ 50 in the first month of this year and increased her monthly saving by ₹ 20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
Write the expression for the common difference of an A.P. whose first term is a and nth term is b.
If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is
Q.18
How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.
The sum of all odd integers between 2 and 100 divisible by 3 is ______.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a + c)(b + c - 2a))/(2(b - a))`
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
