A girl and her uncle build a wooden skateboard ramp together

The Skate Ramp Angles

Zara and Uncle Ray are building a skate ramp. The ramp corner is made of two angle parts. How do the parts fit together to make the whole?

4th Grade Math

Step 1: Add the Angle Parts

0°

30°

60°

90°

Uncle Ray splits the ramp corner into two parts. One angle part measures 30 degrees. The other part measures 60 degrees. On the number line, jump 30, then jump 60 more. How many degrees is the whole angle?

30 + 60 = 90. When an angle is split into parts, the parts add up to the whole. The whole ramp corner measures 90 degrees.

Step 2: Find the Missing Part

The ramp rail meets the ground at a square corner. Perpendicular lines always make a 90 degree angle. One part of this corner measures 65 degrees. What is the missing part?

65° + ? = 90°

To determine a missing part, subtract the known part from the whole. 90 - 65 = 25. The missing part is 25 degrees.

Angles Add Up!

The Big Idea

          Part + Part = Whole angle.

          Whole - Part = Missing part.

          Write an equation with a ? for the unknown angle. Then add or
          subtract to solve it.

Angle measures work just like other numbers. The parts must fit together without overlapping.

See It on a Number Line

0°

45°

90°

135°

180°

A straight line makes a 180 degree angle. Analyze the jumps: four equal jumps of 45 land exactly on 180. So 45 + 45 + 45 + 45 = 180, and 90 + 90 = 180 too.

Watch Out!

A Common Mistake

          Leo's whole angle is 120°. One part is 80°.
          Leo wrote 120 + 80 = 200. That is wrong!
        

Zara says: A part can never be bigger than the whole. When you know the whole, subtract: 120 - 80 = 40. The missing part is 40 degrees.

Solve It!

Two angle parts fit together with no overlap. Find the whole angle.

25° + 45° = ?

25 + 45 = 70. Add the ones: 5 + 5 = 10. Add the tens: 20 + 40 = 60. Then 60 + 10 = 70 degrees.

Word Problem

A paper fan opens 75 degrees. Then it opens 40 degrees more. How far open is the fan now?

75 + 40 = 115. The turns add together: 75 + 40 = 115 degrees open.

What Goes in the Blank?

Two parts make one 90 degree corner. Find the missing part.

32° + ? = 90°

90 - 32 = 58. Check it: 32 + 58 = 90. The missing part is 58 degrees.

Word Problem

Two angles fit together to make a straight line. A straight line measures 180 degrees. One angle is 115 degrees. What is the other angle?

180 - 115 = 65. The other angle is 65 degrees. Check: 115 + 65 = 180.

Turn by Turn

0°

90°

180°

270°

360°

A sprinkler turns 90 degrees, then 90 more, then 90 more. How far has it turned in all?

90 + 90 + 90 = 270. Three jumps of 90 on the number line land on 270 degrees.

Challenge!

Zara paints a round sign with three angle parts. A full circle measures 360 degrees. Two parts measure 150 degrees and 120 degrees. Determine the third part.

150° + 120° + ? = 360°

First add the known parts: 150 + 120 = 270. Then subtract from the whole: 360 - 270 = 90. The third part is 90 degrees.

Where do you see angles that fit together in real life? How could an equation help you find a missing angle?

Great Work!

0/8

correct

angle degree perpendicular analyze determine