Question

In a right triangle, he measure of one acute angle is 3 times the sum of the other acute angle and 8, Find the measure of angle 1 and 2

Answer 1

Let the acute angles be x and y respectively.  x= 3(y+8).

The sum of the interior angles of a triangle is always 180 degrees.  Therefore, 90 + y + 3(y+8) = 180, and so y + 3y + 24 = 90  =>  4y= 66, and y = 66/4 = 16.5 degrees.

Let's check:  If we're right, then y + 3(y+8) = 90
                                                16.5 + 3(16.5 + 8) = 90  ?
                                                 Yes.  (check it yourself)

Thus, the 3 angles of this right triangle are 90, 16.5 and 73.5; they add up to 180 degrees.

Answer 2

The measure of angles 1 and 2 are 16.5 and 73.5 respectively.

The sum of the two acute angles is complementary.

Let the complementary acute angles be x and y

Since they form a right angle triangle, hence;

x  + y = 90 ............................. 1

If the measure of one acute angle is 3 times the sum of the other acute angle and 8, this is expressed as x = 3(y + 8)

Substitute the value of x into the equation 1 as shown:

3(y+8) + y = 90

3y + 24 + y = 90

4y + 24 = 90

4y = 90 - 24

4y = 66

y = 66/4

y = 16.5

Get the other acute angle:

x = 90 - y

x = 90 - 16.5

x = 73.5 degrees

Hence the measure of angles 1 and 2 are 16.5 and 73.5 respectively.

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