3- Triangles

Geometry Level 1

In the figure, points A, B and C are aligned. What is the sum of the angles marked in gray? In Degrees.

I had already posted the same problem before.

The answer is 360.

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5 solutions

Parth Lohomi
Jul 1, 2014

notice that the unshaded angles are on one base thus their sum will be 180 hence the sum of the angles which are shaded id 360

Sara Rowland
Jul 29, 2015

Each triangle contains 180 degrees...so 3*180=540. We are leaving out the straight angle at vertex B. Therefore 540-180=360.

Riska Mulyani
Dec 21, 2014

We know the sum of the angles is 180 in the first triangle, second, and third. So the total is 180 x 3. But there're 3 unshaded angles including, which are the sum is 180. So we must subtract it, (180 x 3)-180 = 180 x 2 = 360

At point B, the 3 angles are not included in gray. We know that the sum of angles in a triangle is 180 degrees. We know that the sum of angles in a straight line is 180 degrees. The centre angle at point B is a common unknown in both the straight line and the triangle; therefore the sum of the 2 shaded angles of the smallest triangle are equal to the missing angles of the larger triangles. Thus the shaded angles are now the all the angles of 2 triangles. There the sum of all angles in 2 triangles = 2 * 180 = 360 degrees.

Krishna Garg
Jul 31, 2014

At point B sum of angles is 180 degree. and therefore sum of all shaded angles will be 180 +180 degrees =360 degrees Ans. K.K.GARG,India

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