In a right triangle, the measure of one acute angle is 2 times the sum of the measure of the other acute angle and 3. Find the measure of each acute angle

Question

I know that the answers are 28 degrees and 62 degrees but I don’t know how to work it out.

Answer 1

In a right triangle we know that one of the angles is 90°. We also know that the 3 angles must add up to 180°.

Let x = acute angle 1

y = acute angle 2

We have 2 unknowns, therefore we must have 2 equations to solve this.

Eq. I Eq. II

90 + x + y = 180 x = 2(y + 3)

x + y = 180 - 90 x = 2y + 6

x + y = 90

Using the value for x in terms of y from Eq. II in Eq. I we can solve for y:

x = 2y + 6 Eq. II

x + y = 90 Eq. I

2y + 6 + y =90 substitute 2y + 6 for x

3y = 90 - 6 add the y terms and subtract 6 from both sides

3y = 84 simplify

y = 84/3 divide both sides by 3

y = 28 solve for y

Using this value for y in Eq. II we can solve for x:

x = 2y + 6 Eq. II

x = 2(28) + 6 substitute 28 for y

x = 56 + 6 simplify

x = 62 solve for x

Therefore, you get the other 2 acute angles as 28° & 62°.