Q. 95.0( 3 Votes )

# If we produce the

Answer :

Given: ΔABC, exterior angles ABD and ACE

To prove: the sum of the measurement of these two exterior angles is more than 2 right angles, i.e., ABD + ACE > 2(90°)

The figure for the given question is as shown below, We know in a triangle the measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.

So in ΔABC ABD and ACE are exterior angles, so

ABD = BAC + ACB……..(i)

And,

ACE = ABC + BAC……..(ii)

Adding equation (i) an equation (ii), we get

ABD + ACE = BAC + ACB + ABC + BAC …….(iii)

We also know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

BAC + ACB + ABC = 180°

Substituting the above equation in equation (iii), we get

ABD + ACE = (BAC + ACB + ABC) + BAC

ABD + ACE = (180°) + BAC

ABD + ACE > 180°

ABD + ACE > 2(90°)

Hence the sum of the measurement of these two exterior angles is more than 2 right angles.

Hence proved

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