It looks like you've uploaded a worksheet titled
"Finding Supplementary Angles", which contains several problems involving supplementary angles. Let's go through the concept and solve each problem step-by-step.
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🔹 What Are Supplementary Angles?
Supplementary angles are two angles whose measures add up to
180 degrees.
So, if one angle is given, and you're told the other is supplementary, you can find it using:
\[
x = 180^\circ - \text{given angle}
\]
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Now let’s analyze each problem in the image:
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✔ Problem 1:
- Given: One angle is \(100^\circ\)
- Find: \(x\)
\[
x = 180^\circ - 100^\circ = 80^\circ
\]
✔ Answer: \(x = 80^\circ\)
---
✔ Problem 2:
- Given: One angle is \(75^\circ\)
- Find: \(x\)
\[
x = 180^\circ - 75^\circ = 105^\circ
\]
✔ Answer: \(x = 105^\circ\)
---
✔ Problem 3:
- Given: One angle is \(34^\circ\)
- Find: \(x\)
\[
x = 180^\circ - 34^\circ = 146^\circ
\]
✔ Answer: \(x = 146^\circ\)
---
✔ Problem 4:
- Given: One angle is \(115^\circ\)
- Find: \(x\)
\[
x = 180^\circ - 115^\circ = 65^\circ
\]
✔ Answer: \(x = 65^\circ\)
---
✔ Problem 5:
- Given: One angle is \(163^\circ\)
- Find: \(x\)
\[
x = 180^\circ - 163^\circ = 17^\circ
\]
✔ Answer: \(x = 17^\circ\)
---
✔ Problem 6:
- Given: One angle is \(80^\circ\)
- Find: \(x\)
\[
x = 180^\circ - 80^\circ = 100^\circ
\]
✔ Answer: \(x = 100^\circ\)
---
✔ Problem 7:
- Given: One angle is \(48^\circ\)
- Find: \(x\)
\[
x = 180^\circ - 48^\circ = 132^\circ
\]
✔ Answer: \(x = 132^\circ\)
---
✔ Problem 8:
- Given: One angle is \(107^\circ\)
- Find: \(x\)
\[
x = 180^\circ - 107^\circ = 73^\circ
\]
✔ Answer: \(x = 73^\circ\)
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📌 Summary of Answers:
| Problem | Given Angle | Supplementary Angle (x) |
|--------|-------------|-------------------------|
| 1 | 100° | 80° |
| 2 | 75° | 105° |
| 3 | 34° | 146° |
| 4 | 115° | 65° |
| 5 | 163° | 17° |
| 6 | 80° | 100° |
| 7 | 48° | 132° |
| 8 | 107° | 73° |
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✔ Final Notes:
All these problems are straightforward applications of the
supplementary angle rule:
> If two angles form a straight line (or are supplementary), their sum is \(180^\circ\).
So, whenever you see two angles next to each other forming a straight line, use:
\[
x = 180^\circ - \text{known angle}
\]
Let me know if you'd like this formatted as a printable PDF or need help with another type of angle problem!
Parent Tip: Review the logic above to help your child master the concept of supplementary angles worksheet to print.
