Question

A quadrilateral has angle in the ratio 1:2:3 and a fourth angle is 31 degrees larger than the smallest angle.Find the sum of second smallest and second largest angle?

Answer 1

Step-by-step explanation:

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Answer 2

Given:

A quadrilateral has an angle in the ratio 1:2:3 and a fourth angle is 31 degrees larger than the smallest angle.

To find:

We have to find the sum of the second smallest and second-largest angles.

Solution:

A quadrilateral has an angle in the ratio 1:2:3 and a fourth angle is 31 degrees larger than the smallest angle.

Let the angles be 1x, 2x and 3x.

The smallest angle is 1x.

Thus, the fourth angle is x+31°.

We know that the sum of four angles in a quadrilateral is 360°.

So, we can write-

$x + 2x + 3x + x + 31 = 360 \\ 7x = 329 \\ x = 47$

Thus, the angles are-

47°, 2×47°, 3×47° and 47+31°.

=47°, 94°, 141° and 78°.

The second smallest angle is 78° and the second-largest angle is 94°.

So, the sum of the second smallest and second-largest angles is 94°+78°=172°.