Which angle is equal to twice its complement?

That Tricky Angle: When It’s Twice Its Complement

Angles. We learn about them in school, but they pop up everywhere, right? From the corners of your phone to the way a bridge is built, angles are fundamental. And one of the handiest relationships between angles is the idea of “complementary angles” – two angles that team up to make a perfect 90-degree angle. But things get really interesting when you ask: what if an angle is twice the size of its partner? Let’s dive in and figure it out.

Complementary Angles: A Quick Refresher

Okay, so what exactly are complementary angles? Think of a perfectly square corner – that’s 90 degrees. Now, split that corner into two smaller angles. Bam! You’ve got complementary angles. They just have to add up to 90 degrees. A classic example? A 30-degree angle and a 60-degree angle. Simple as that!

In math-speak, if you’ve got angle A and angle B, they’re complementary when:

Angle A + Angle B = 90°

The Real Puzzle: Double Trouble

Alright, let’s get to the good stuff. We’re hunting for an angle that’s twice the size of its complement. Sounds like a riddle, doesn’t it? This is a pretty common geometry brain-teaser, and we can crack it with a little algebra. Don’t worry, it’s not as scary as it sounds!

Here’s how we’ll break it down:

• Let’s call the angle we’re looking for “x”.
• That means its complement is “(90 – x)” – because, remember, they have to add up to 90 degrees!

So, the problem tells us that our angle “x” is double its complement. We can write that as:

x = 2 * (90 – x)

Cracking the Code

Time to put on our algebra hats! Let’s solve for “x”:

Boom! The angle we’re looking for is 60 degrees.

Does It Add Up?

Let’s make sure we didn’t mess anything up.

• Our angle is 60 degrees.
• That means its complement is (90 – 60) = 30 degrees.
• Is 60 degrees twice as big as 30 degrees? You bet! 60 = 2 * 30.

The Big Picture

So, the answer is 60 degrees. This little problem is a great example of how geometry and algebra work together. Understanding how angles relate to each other is super useful, not just in math class, but in all sorts of real-world situations. Think about architects designing buildings, or engineers building bridges – they’re using these principles every single day. Pretty cool, huh?