Question

The difference between the measures of the two angles of a complementary pair is  40^°. Find the measures of the two angles.

Answer 1

Let the measure of the first angle x.

Then, the measure of the other angle x + 40^°

Now, x^° + (x + 40)^° = 90^°   ...(Since, the two angles are complementary)

∴ 2x^° + 40^° − 40^° = 90^° − 40   ...(Subtracting 40 from both sides)

∴ 2x^° = 50^°

∴ `x^circ = 50/2`

∴ x^° = 25^°

∴ x + 40^°

= 25^° + 40^°

= 65^°

Hence, the measures of the two angles are 25^° and 65^°.

Answer 2

Step 1: Use the definition of complementary angles

x + y = 90^∘

Step 2: Use the given difference between the angles

x − y = 40^∘

Step 3: Solve the system of equations

We have:

1. x + y = 90^°
2. x − y = 40^°

Add the two equations:

(x + y) + (x − y) = 90^° + 40^°

2x^° = 130^°

x^° = 65^∘

Substitute x = 65^° into the first equation:

65^° + y = 90^°

y = 25^°

The two angles are 65^° and 25^°.