Question

11. An acute angle of a right angle triangle measures 12 degree less than the other acute angle find the measure of both the angles.

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Answer 1

Answer:

One Angle is 51° and other angle is 39°

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Answer 2

Given :-

Measure of the first angle of this triangle =90°

Let the measure of it's second angle be x.

Then, the measure of it's third angle= x-12

The sum of the measures of all three angles of this triangle =180°(angle sum property)

Let us solve :-

$= 90 + x + x - 12 = 180$

$= 90 + 2x - 12 = 180$

$= 90 + 2x = 180 + 12$

$= 90 + 2x = 192$

$= 2x = 192 - 90$

$= 2x = 102$

$= x = \frac{102}{2}$

$= x = 51$

Which means :-

Angle one :-

$=\bold{ 90°}$

Angle two :-

$= \bold{51°}$

Angle three :-

$= 51 - 12$

$=\bold{ 39°}$

As the sum of all three interior angles of this right angle triangle is adding up to form 180°, we can conclude that we have found out the correct measure of each of the acute angles of this triangle.

Therefore, the measure of the two acute angles of this triangle =51° and 39° ,The third angle is a right angle which means it's measure will be equal to 90° .