Prove that a triangle must have two acute angle
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The sum of all 3 angles of triangle is always 180 degrees doesn't matter what type of triangle it is.
An acute is less than 90 degree.
Let us assume two angle of triangle to be greater than 90 degree and 3rd angle x.(Let two angles be 91 degree which is greater than acute angle).
Then sum of three angles of triangle will be
91 + 91 + x=182 + x
So, sum is greater than 180 degree which is not possible.
Hence,we contradict our assumption.
An acute is less than 90 degree.
Let us assume two angle of triangle to be greater than 90 degree and 3rd angle x.(Let two angles be 91 degree which is greater than acute angle).
Then sum of three angles of triangle will be
91 + 91 + x=182 + x
So, sum is greater than 180 degree which is not possible.
Hence,we contradict our assumption.
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LET A TRIANGLE BE ΔABC
SO THE SUM OF ALL SIDES SHOULD BE =180 °
SO ,∠A+∠B+∠C=180°
IF ALL ANGLES ARE ABOVE 90° THE SUM WILL BE GREATER THAN 180°
TAKE AN ANGLE AS 100° SO REST TWO ANGLES SHOULS BE LESS THAN 80°AS TO BECOME EQUAL TO 180°
SO AS PER THIS CASE TWO ANGLS ARE ACUTE AS THEY ARE LESS THAN 80° AND 80°IS LESS THAN 90°
ANOTHER EXAMPLE TAKE AN ANGLE AS 90° SO THE OTHER TWO ANGLES WILL BE ACUTE AND LESS THAN 90° TO MAKE A SUM TOTAL OF180°
SO THE SUM OF ALL SIDES SHOULD BE =180 °
SO ,∠A+∠B+∠C=180°
IF ALL ANGLES ARE ABOVE 90° THE SUM WILL BE GREATER THAN 180°
TAKE AN ANGLE AS 100° SO REST TWO ANGLES SHOULS BE LESS THAN 80°AS TO BECOME EQUAL TO 180°
SO AS PER THIS CASE TWO ANGLS ARE ACUTE AS THEY ARE LESS THAN 80° AND 80°IS LESS THAN 90°
ANOTHER EXAMPLE TAKE AN ANGLE AS 90° SO THE OTHER TWO ANGLES WILL BE ACUTE AND LESS THAN 90° TO MAKE A SUM TOTAL OF180°
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