Two supplementary angles differ by 48°. Find the angles.

To find two supplementary angles that differ by 48°, we can set up a simple equation. Supplementary angles add up to 180°.

Setting Up the Equations

Let one angle be represented as x. The other angle, which is 48° less, can be expressed as x - 48.

Equation for Supplementary Angles

Since the angles are supplementary, we can write the equation:

• x + (x - 48) = 180

Solving the Equation

Now, let's simplify and solve for x:

• 2x - 48 = 180
• 2x = 180 + 48
• 2x = 228
• x = 114

Finding the Second Angle

Now that we have the first angle:

• First angle: 114°
• Second angle: 114° - 48° = 66°

Final Result

The two supplementary angles are 114° and 66°.