Q18 of 90 Page 111

Two angles of a triangle are in the ratio 4: 5. If the sum of these angles is equal to the third angle, find the angles of the triangle.

Let the given two angles of a triangle be 4x and 5x


According to the question


3rd angle = 4x + 5x = 9x


Using angle sum property of a triangle


4x + 5x + 9x = 180°


⇒ 18x = 180°


⇒ x = 10


So, the angles of the given triangle are:


4x = 40, 5x = 50 and 9x = 90


More from this chapter

All 90 →
16

The width of a rectangle is two - thirds its length. If the perimeter is 180 metres, find the dimensions of the rectangle.

 17

An altitude of a triangle is five - thirds the length of its corresponding base. If the altitude be increased by 4 cm and the base decreased by 2 cm, the area of the triangle remains the same. Find the base and the altitude of the triangle.

 19

A steamer goes downstream from one port to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/h, find the speed of the steamer in still water and the distance between the ports.

 20

The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist. Check your solution.