Angles in a Triangle Worksheets - Math Monks - Free Printable

This is a worksheet titled "Angles in a Triangle Worksheet" that asks to find the missing angles, labeled as 'x', in eight different triangles. To solve this, I will use the fundamental geometric principle that the sum of the interior angles in any triangle is always 180 degrees.

I will solve each problem one by one.

---

Problem 1:
The given angles are 45° and 65°.
- The equation is: $x + 45 + 65 = 180$
- Simplifying: $x + 110 = 180$
- Solving for x: $x = 180 - 110 = 70$
- Answer: x = 70°

---

Problem 2:
The given angle is 138°, and the other two angles are both 'x'.
- The equation is: $x + x + 138 = 180$
- Simplifying: $2x + 138 = 180$
- Subtracting 138 from both sides: $2x = 42$
- Solving for x: $x = 42 / 2 = 21$
- Answer: x = 21°

---

Problem 3:
This is a right triangle with angles 90° and 20°.
- The equation is: $x + 90 + 20 = 180$
- Simplifying: $x + 110 = 180$
- Solving for x: $x = 180 - 110 = 70$
- Answer: x = 70°

---

Problem 4:
All three angles are labeled 'x', meaning it's an equilateral triangle.
- The equation is: $x + x + x = 180$
- Simplifying: $3x = 180$
- Solving for x: $x = 180 / 3 = 60$
- Answer: x = 60°

---

Problem 5:
The given angles are 65° and 65°.
- The equation is: $x + 65 + 65 = 180$
- Simplifying: $x + 130 = 180$
- Solving for x: $x = 180 - 130 = 50$
- Answer: x = 50°

---

Problem 6:
This is a right triangle with a 90° angle.
- The equation is: $x + x + 90 = 180$
- Simplifying: $2x + 90 = 180$
- Subtracting 90 from both sides: $2x = 90$
- Solving for x: $x = 90 / 2 = 45$
- Answer: x = 45°

---

Problem 7:
The given angles are 69° and 33°.
- The equation is: $x + 69 + 33 = 180$
- Simplifying: $x + 102 = 180$
- Solving for x: $x = 180 - 102 = 78$
- Answer: x = 78°

---

Problem 8:
The given angles are 113° and 15°.
- The equation is: $x + 113 + 15 = 180$
- Simplifying: $x + 128 = 180$
- Solving for x: $x = 180 - 128 = 52$
- Answer: x = 52°

---

Final Answers:

1. 70°
2. 21°
3. 70°
4. 60°
5. 50°
6. 45°
7. 78°
8. 52°