Question

The measures of one acute angle in a right triangle is four times the measure of the other acute

angle. Write and solve a system of equations to find the measures of the acute angles.

Help with this exercise

Answer 1

`A_2` = 18°

`A_3` = 4(18°) = 72°

Explanation:

Given:

1. One angle in the triangle is 90°
2. One angle that isn't 90° is 4 times larger than another angle that isn't 90°

Angles:

`A_1` = 90°

`A_2` = x

`A_3` = 4x

Solution Pathway:

Under the rules for any triangle, a triangle's interior angles must add up to 180°. Using this, we can set up the equation:

• sum of the interior angles = 180°

• 90° + x + 4x = 180°

Now let's solve for x.

• 90 +x + 4x = 180
• 90 + 5x = 180
• 5x = 90
• x = 18°

Now that we know x is 18°, lets plug this value into the two unknown acute angles.

• 
  `A_2` = 18°

• 
  `A_3` = 4(18°) = 72°

Answer 2

72 degrees and 18 degrees.

Explanation:

If the 2 angles are x and y, we have the system:

x + y = 90 (as it is a right triangle)

x = 4y (given).

Substitute x =- 4y in the first equation:

4y + y = 90

5y = 90

y = 18.

So x + 18 = 90

x = 90 - 18

x = 72.