The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the ...

Question

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3 : 5 : 6 : 8. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the second largest angle of the quadrilateral?

Accepted Answer

180 degrees A quadrilateral's angles are in ratio 3:5:6:8 and must sum to 360 degrees, giving us each angle. Two-thirds of the smallest quadrilateral angle equals the smallest triangle angle. With the triangle's largest angle twice its smallest, we find all three triangle angles by using the 180-degree angle sum. The required sum turns out to be exactly 180 degrees.