Question

In a right triangle, the measure of one acute angle is 2 times the sum of the measure of the other acute angle and 6. find the measure of each acute angle.

Answer 1

Let one acute angle be x

The other acute angle = 2(x + 6)

The sum of all the 3 angles in a triangle add up to 180

x + 2(x+ 6) + 90 = 180

x + 2x + 12 + 90 = 180

3x + 102 = 180

3x = 78

x = 26

one acute angle = x = 26

the other acute angle = 2(x + 6) = 2(26 + 6) = 64

Answer: The two acute angles are 26° and 64°

Answer 2

In this right triangle, the measure of each acute angle is 26 and 64 degrees respectively.

• Let the acute angle be a.

We know that a right triangle is equal to 90 degrees.

Translating the word problem into an algebraic expression, we have;

The measure of one acute angle is 2 times the sum of the measure of the other acute angle and 6:

$2(a+6)$

To find the measure of each acute angle, we would sum all the interior angles together to equal 180 degrees:

$a + 2(a+6) + 90 = 180\\\\a+2a+12+90=180\\\\3a+102=180\\\\3a = 180-102\\\\3a=78\\\\a=\frac{78}{3}$

a = 26°

For the second acute angle:

$2(a+6)\\\\2(26+6)\\\\2(32) = 64 \;degrees$

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