To solve each problem, we use the
Triangle Angle Sum Theorem, which states:
>
The sum of the interior angles in any triangle is always 180°.
So for each triangle, if two angles are given, we subtract their sum from 180° to find the missing angle.
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Let’s go through each one:
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1) Triangle TUV
Given: ∠T = 37°, ∠V = 63°
Find: m∠U
Solution:
m∠U = 180° - (37° + 63°) = 180° - 100° =
80°
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2) Triangle ABC (right triangle at C)
Given: ∠C = 90° (right angle), ∠A = 46°
Find: m∠B
Solution:
m∠B = 180° - (90° + 46°) = 180° - 136° =
44°
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3) Triangle PQR
Given: ∠P = 51°, ∠R = 36°
Find: m∠Q
Solution:
m∠Q = 180° - (51° + 36°) = 180° - 87° =
93°
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4) Triangle EFG
Given: ∠G = 86°, ∠E = 47°
Find: m∠F
Solution:
m∠F = 180° - (86° + 47°) = 180° - 133° =
47°
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5) Triangle XYZ
Given: ∠Z = 118°, ∠X = 33°
Find: m∠Y
Solution:
m∠Y = 180° - (118° + 33°) = 180° - 151° =
29°
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6) Triangle UVW
Given: ∠W = 42°, ∠U = 64°
Find: m∠V
Solution:
m∠V = 180° - (42° + 64°) = 180° - 106° =
74°
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7) Triangle KLM
Given: ∠L = 60°, ∠M = 60°
Find: m∠K
Solution:
m∠K = 180° - (60° + 60°) = 180° - 120° =
60°
*(This is an equilateral triangle — all angles equal!)*
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8) Triangle STU
Given: ∠S = 35°, ∠T = 35°
Find: m∠U
Solution:
m∠U = 180° - (35° + 35°) = 180° - 70° =
110°
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9) Triangle CDE
Given: ∠E = 53°, ∠D = 77°
Find: m∠C
Solution:
m∠C = 180° - (53° + 77°) = 180° - 130° =
50°
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✔ Final Answers:
1)
m∠U = 80°
2)
m∠B = 44°
3)
m∠Q = 93°
4)
m∠F = 47°
5)
m∠Y = 29°
6)
m∠V = 74°
7)
m∠K = 60°
8)
m∠U = 110°
9)
m∠C = 50°
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Let me know if you’d like a diagram or step-by-step visual explanation for any of these!
Parent Tip: Review the logic above to help your child master the concept of calculating angles worksheet.
