Question

Smallest angle of a triangle is equal to two-third the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3 :4 : 5 : 6. Largest angle of the triangle is twice its smallest angle. What is the sum of second largest angle of the triangle and largest angle of the quadrilateral ?

Answer 1

Answer:

180°

Step-by-step explanation:

First, find angles of quadrilateral.

Let the angles be 3x, 4x, 5x and 6x.

Sum = 360°.

3x + 4x + 5x + 6x = 360°.

18x = 360°.

x = 360 ÷ 18

x = 20°.

Angles = 3x = 3 × 20 = 60°

4x = 4 × 20 = 80°

5x = 5 × 20 = 100°

6x = 6 × 20 = 120°

Smallest angle of triangle is 2/3rd of smallest angle of quadrilateral.

= 2/3 × 60 = 40°.

Largest angle of triangle is twice of the smallest angle

= 40 × 2 = 80°.

Let the second largest angle of triangle be x

40° + 80° + x = 180°.

120° + x = 180°.

x = 180° - 120°.

x = 60°.

Largest angle of quadrilateral = 120°.

Their sum = 120° + 60° = 180°.

Therefore, the final answer is 180°.