The angles of a triangle are in AP. If it's greatest angle is equal the sum of the other two. Find the angles.
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Let the measure of least angle be x
and the measure of greatest angle = x+remaining angle
as, we know that, sum of all angles of a tr. = 180 degree
therefore,
x+remaining angle +x+remaining angle = 180°
2x+2 (remaining angle) = 180°
x+remaining angle = 90°
remaining angle = 90°-x
the measure of greatest angle = x+90°-x=90°
acc. to the question,
x, 90°-x, 90° are in A.P.
In an A.P. , the difference b/w two consecutive terms is constant.
90°-x-x=90°-90°+x
90°-2x=x
90°=x+2=3x
or x=30°
thus, the measure of the angles of triangle are 30°,60° and 90°
and the measure of greatest angle = x+remaining angle
as, we know that, sum of all angles of a tr. = 180 degree
therefore,
x+remaining angle +x+remaining angle = 180°
2x+2 (remaining angle) = 180°
x+remaining angle = 90°
remaining angle = 90°-x
the measure of greatest angle = x+90°-x=90°
acc. to the question,
x, 90°-x, 90° are in A.P.
In an A.P. , the difference b/w two consecutive terms is constant.
90°-x-x=90°-90°+x
90°-2x=x
90°=x+2=3x
or x=30°
thus, the measure of the angles of triangle are 30°,60° and 90°
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