To solve for
x in each triangle, we use the fundamental property:
>
The sum of the interior angles of any triangle is always 180°.
We’ll go one by one.
---
1) Triangle with angles: 58°, 47°, x°
Equation:
58 + 47 + x = 180
105 + x = 180
x = 180 - 105 =
75
✔ Answer: x = 75
---
2) Triangle with angles: x°, 96°, 21°
Equation:
x + 96 + 21 = 180
x + 117 = 180
x = 180 - 117 =
63
✔ Answer: x = 63
---
3) Right triangle with angles: 90°, 31°, (3x - 1)°
Equation:
90 + 31 + (3x - 1) = 180
120 + 3x = 180
3x = 60
x =
20
✔ Answer: x = 20
---
4) Triangle with angles: 21°, 34°, x° (exterior angle shown, but we need interior)
Wait — the diagram shows an
exterior angle at one vertex. But the question asks for
x°, which appears to be the
interior angle adjacent to the exterior angle.
Actually, looking closely — the angle marked
x° is an
interior angle of the triangle. The arrow pointing left is just indicating the direction, not that it’s an exterior angle.
So: 21° + 34° + x° = 180°
55 + x = 180
x =
125
✔ Answer: x = 125
*(Note: If x were the exterior angle, it would be 21+34=55, but since it's labeled inside the triangle, it’s interior.)*
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5) Triangle with angles: 100°, (2x + 3)°, 51°
Equation:
100 + (2x + 3) + 51 = 180
154 + 2x = 180
2x = 26
x =
13
✔ Answer: x = 13
---
6) Triangle with angles: 94°, 60°, 2x°
Equation:
94 + 60 + 2x = 180
154 + 2x = 180
2x = 26
x =
13
✔ Answer: x = 13
---
7) Triangle with angles: 52°, 43°, x°
Equation:
52 + 43 + x = 180
95 + x = 180
x =
85
✔ Answer: x = 85
---
8) Triangle with angles: x°, 2x°, 3x°
Equation:
x + 2x + 3x = 180
6x = 180
x =
30
✔ Answer: x = 30
---
9) Right triangle with angles: 90°, (2x - 2)°, (x + 5)°
Equation:
90 + (2x - 2) + (x + 5) = 180
90 + 2x - 2 + x + 5 = 180
93 + 3x = 180
3x = 87
x =
29
✔ Answer: x = 29
---
10) Triangle with angles: 10°, 23°, x°
Equation:
10 + 23 + x = 180
33 + x = 180
x =
147
✔ Answer: x = 147
---
11) Equilateral triangle? All angles are x°
Equation:
x + x + x = 180
3x = 180
x =
60
✔ Answer: x = 60
---
12) Triangle with angles: (x + 40)°, (3x - 17)°, (2x - 5)°
Equation:
(x + 40) + (3x - 17) + (2x - 5) = 180
Combine like terms:
x + 3x + 2x + 40 - 17 - 5 = 180
6x + 18 = 180
6x = 162
x =
27
✔ Answer: x = 27
---
##
✔ Final Answers:
1)
75
2)
63
3)
20
4)
125
5)
13
6)
13
7)
85
8)
30
9)
29
10)
147
11)
60
12)
27
Let me know if you’d like diagrams or step-by-step visuals for any!
Parent Tip: Review the logic above to help your child master the concept of angle sum theorem worksheet.
