Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
In an AP given d = 5, S9 = 75, find a and a9.
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
Find the sum of the odd numbers between 0 and 50.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
Find the sum of all 3 - digit natural numbers which are divisible by 13.
The angles of quadrilateral are in whose AP common difference is 10° . Find the angles.
If the numbers a, 9, b, 25 from an AP, find a and b.
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
Q.2
Q.12
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
If Sn denotes the sum of first n terms of an AP, prove that S12 = 3(S8 – S4)
Find the sum of first seven numbers which are multiples of 2 as well as of 9.
Find the value of a25 – a15 for the AP: 6, 9, 12, 15, ………..
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))`.
