The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The ...
Option C
The largest angle of the quadrilateral =
= 120°
The smallest angle of the triangle = 120 ×(1/4) = 30°
If the second largest angle of the triangle be x°, then the largest angle of the triangle = (x° + 10°)
30 + x + x + 10 = 180 x = 70°
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The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The ...
Given data:
Ratio of angles of quadrilateral = 6 : 3 : 4 : 5
Let the angles of the quadrilateral be 6x, 3x, 4x and 5x respectively.
Also, the smallest angle of the triangle = (1/4) × largest angle of the quadrilateral = (1/4) × 5x = (5/4)x
Let the angles of the triangle be a, b and c such that a ≤ b ≤ c.
Also, c = 10 + b.
We need to find the value of b.
Approach:
The sum of angles of a quadrilateral is 360°.
Hence, we can find the value of x and the angles of the quadrilateral.
Using the given information, we can also find the value of (5/4)x.
Further, we can use the fact that the sum of angles of a triangle is 180° to find the value of c and hence, b.
Calculation:
Let us first find the value of x.
6x + 3x + 4x + 5x = 360°
18x = 360°
x = 20°
Hence, the angles of the quadrilateral are:
6x = 120°
3x = 60°
4x = 80°
5x = 100°
Smallest angle of the triangle = (5/4)x = (5/4) × 20° = 25°
Let us denote the angles of the triangle as a, b and c such that a ≤ b ≤ c.
Also, c = 10 + b.
a + b + c = 180°
a + b + (b + 10) = 180°
2b + 10 + a = 180°
a + 2b = 170°
Since a ≤ b ≤ c, we have:
a + b > c
a + b > b + 10
a > 10
Hence, the possible values of a and b are:
a = 11°, b = 79.5°, c = 89.5°
a = 12°, b = 79°, c = 89°
a = 13°, b = 78.5°, c = 88.5°
a = 14°, b = 78°, c = 88°
...
a = 78°, b = 46°, c = 56°
a = 79°, b = 45.5°, c = 55.5°
a = 80°, b = 45°, c = 55°
Since the largest angle of the triangle is 80°, the second largest angle is 45°.
Hence, the correct answer is option (c) 70.
The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The ...
Answer ( C )