1. Suppose that in a certain triangle, the degree measures of the interior angles are in the ratio 2:3:4.If the largest interior angle measures x degrees, what is the value of ?
I'm assuming that you want the value of the largest angle....the sum of the interior angles of a triangle = 180° ... and the ratio of 2:3:4 indicates that there there are 9 equal parts of the180°......the largest angle is 4/9ths of this = (4/9) (180) = 80°
2.Suppose that in a certain triangle, the degree measures of the exterior angles are in the ratio 2:3:4.
If the largest interior angle measures x degrees, what is the value of ?( x degrees)
The sum of the exteriior angles of any regular polygon total 360°.......as before, there are 9 equal parts of the 360°....the largest interior angle will be supplementary to the smallest exterior angle.......the smallest exterior angle = (2/9) (360) = 80°....so the greatest interior angle will = 180 - 80 = 100°
Proof of this is that the next greatest exteriior angle = (3/9)(360) = 120° and the interior angle supplementary to this = 180 - 120 = 60°
And the greatest exterior angle = ( 4/9) (360) = 160°....and the interior angle supplementary to this = 180 - 160 = 20°
And the sum of the interior angles is 100 + 60 + 20 = 180°
Thanks to the guest for spotting my previous error.....!!!!!