If three angles of a triangle are in the ratio 3:7:10 show that triangle is right angled

Let the angles be 3x, 7x and 10x.
By the Angle Sum Property of triangle,
3x+7x+10x = 180 (degrees)
=> 20x = 180
=> x = 180/20
=> x = 9
Now,
The first angle = 3x = 3(9)
                        = 27 degrees.
The second angle = 7x = 7(9)
                              = 63 degrees
the third angle = 10x = 10(9)
                        = 90 degrees.
Therefore, the triangle includes a right angle, and two acute angles. Hence, it is a right triangle
H.P.
  • 2
3x +7x + 10x =180 So 20x=180 Now x = 180÷20 Now x=9 So 3x9 =27 7x9 =63 10×9=90
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