Calculating the Missing Angle in a Triangle worksheet | Live ... - Free Printable

To solve the problem of finding the missing angles in each triangle, we use the fundamental property that the sum of the interior angles of a triangle is always 180°. Let's go through each triangle step by step.

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1)

Triangle with vertices \( T, U, V \):
- Given angles: \( \angle T = 37^\circ \), \( \angle V = 63^\circ \)
- To find: \( \angle U \)

Using the angle sum property:
\[
\angle T + \angle U + \angle V = 180^\circ
\]
\[
37^\circ + \angle U + 63^\circ = 180^\circ
\]
\[
100^\circ + \angle U = 180^\circ
\]
\[
\angle U = 180^\circ - 100^\circ = 80^\circ
\]

Answer: \( m\angle U = 80^\circ \)

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2)

Triangle with vertices \( A, B, C \):
- Given angles: \( \angle A = 46^\circ \), \( \angle C = 90^\circ \) (right angle)
- To find: \( \angle B \)

Using the angle sum property:
\[
\angle A + \angle B + \angle C = 180^\circ
\]
\[
46^\circ + \angle B + 90^\circ = 180^\circ
\]
\[
136^\circ + \angle B = 180^\circ
\]
\[
\angle B = 180^\circ - 136^\circ = 44^\circ
\]

Answer: \( m\angle B = 44^\circ \)

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3)

Triangle with vertices \( P, Q, R \):
- Given angles: \( \angle P = 51^\circ \), \( \angle R = 36^\circ \)
- To find: \( \angle Q \)

Using the angle sum property:
\[
\angle P + \angle Q + \angle R = 180^\circ
\]
\[
51^\circ + \angle Q + 36^\circ = 180^\circ
\]
\[
87^\circ + \angle Q = 180^\circ
\]
\[
\angle Q = 180^\circ - 87^\circ = 93^\circ
\]

Answer: \( m\angle Q = 93^\circ \)

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4)

Triangle with vertices \( E, F, G \):
- Given angles: \( \angle G = 86^\circ \), \( \angle E = 47^\circ \)
- To find: \( \angle F \)

Using the angle sum property:
\[
\angle G + \angle F + \angle E = 180^\circ
\]
\[
86^\circ + \angle F + 47^\circ = 180^\circ
\]
\[
133^\circ + \angle F = 180^\circ
\]
\[
\angle F = 180^\circ - 133^\circ = 47^\circ
\]

Answer: \( m\angle F = 47^\circ \)

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5)

Triangle with vertices \( X, Y, Z \):
- Given angles: \( \angle Z = 118^\circ \), \( \angle X = 33^\circ \)
- To find: \( \angle Y \)

Using the angle sum property:
\[
\angle Z + \angle Y + \angle X = 180^\circ
\]
\[
118^\circ + \angle Y + 33^\circ = 180^\circ
\]
\[
151^\circ + \angle Y = 180^\circ
\]
\[
\angle Y = 180^\circ - 151^\circ = 29^\circ
\]

Answer: \( m\angle Y = 29^\circ \)

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6)

Triangle with vertices \( U, V, W \):
- Given angles: \( \angle W = 42^\circ \), \( \angle U = 64^\circ \)
- To find: \( \angle V \)

Using the angle sum property:
\[
\angle W + \angle V + \angle U = 180^\circ
\]
\[
42^\circ + \angle V + 64^\circ = 180^\circ
\]
\[
106^\circ + \angle V = 180^\circ
\]
\[
\angle V = 180^\circ - 106^\circ = 74^\circ
\]

Answer: \( m\angle V = 74^\circ \)

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7)

Triangle with vertices \( K, L, M \):
- Given angles: \( \angle L = 60^\circ \), \( \angle M = 60^\circ \)
- To find: \( \angle K \)

Using the angle sum property:
\[
\angle L + \angle K + \angle M = 180^\circ
\]
\[
60^\circ + \angle K + 60^\circ = 180^\circ
\]
\[
120^\circ + \angle K = 180^\circ
\]
\[
\angle K = 180^\circ - 120^\circ = 60^\circ
\]

Answer: \( m\angle K = 60^\circ \)

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8)

Triangle with vertices \( S, T, U \):
- Given angles: \( \angle S = 35^\circ \), \( \angle T = 35^\circ \)
- To find: \( \angle U \)

Using the angle sum property:
\[
\angle S + \angle U + \angle T = 180^\circ
\]
\[
35^\circ + \angle U + 35^\circ = 180^\circ
\]
\[
70^\circ + \angle U = 180^\circ
\]
\[
\angle U = 180^\circ - 70^\circ = 110^\circ
\]

Answer: \( m\angle U = 110^\circ \)

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9)

Triangle with vertices \( C, D, E \):
- Given angles: \( \angle E = 53^\circ \), \( \angle D = 77^\circ \)
- To find: \( \angle C \)

Using the angle sum property:
\[
\angle E + \angle C + \angle D = 180^\circ
\]
\[
53^\circ + \angle C + 77^\circ = 180^\circ
\]
\[
130^\circ + \angle C = 180^\circ
\]
\[
\angle C = 180^\circ - 130^\circ = 50^\circ
\]

Answer: \( m\angle C = 50^\circ \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1) & \, m\angle U = 80^\circ \\
2) & \, m\angle B = 44^\circ \\
3) & \, m\angle Q = 93^\circ \\
4) & \, m\angle F = 47^\circ \\
5) & \, m\angle Y = 29^\circ \\
6) & \, m\angle V = 74^\circ \\
7) & \, m\angle K = 60^\circ \\
8) & \, m\angle U = 110^\circ \\
9) & \, m\angle C = 50^\circ
\end{aligned}
}
\]