Angles on Parallel Lines (C) Worksheet | Cazoom Maths Worksheets - Free Printable

To solve the missing angles in the given diagrams, we will use properties of parallel lines and transversals, as well as basic angle relationships such as supplementary, complementary, and corresponding angles. Let's go through each diagram step by step.

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Diagram 1:

- Given: \(51^\circ\)
- To find: \(a\)

Solution:
- The angle \(a\) is a corresponding angle to the given \(51^\circ\) angle because they are on the same side of the transversal and between the parallel lines.
- Therefore, \(a = 51^\circ\).

Answer: \(a = 51^\circ\)

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Diagram 2:

- Given: \(104^\circ\) and \(117^\circ\)
- To find: \(b\) and \(c\)

Solution:
- The angle \(b\) is a corresponding angle to the given \(104^\circ\) angle.
\[
b = 104^\circ
\]
- The angle \(c\) is a corresponding angle to the given \(117^\circ\) angle.
\[
c = 117^\circ
\]

Answers: \(b = 104^\circ\), \(c = 117^\circ\)

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Diagram 3:

- Given: \(67^\circ\) and \(75^\circ\)
- To find: \(d\) and \(e\)

Solution:
- The angle \(d\) is an alternate interior angle to the given \(67^\circ\) angle.
\[
d = 67^\circ
\]
- The angle \(e\) is a corresponding angle to the given \(75^\circ\) angle.
\[
e = 75^\circ
\]

Answers: \(d = 67^\circ\), \(e = 75^\circ\)

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Diagram 4:

- Given: A triangle with one angle \(g\) and another angle formed by a transversal.
- To find: \(f\) and \(g\)

Solution:
- The angle \(f\) is a corresponding angle to the given \(67^\circ\) angle (from the previous diagram).
\[
f = 67^\circ
\]
- The angle \(g\) is the third angle in the triangle. The sum of the angles in a triangle is \(180^\circ\). The other two angles in the triangle are \(67^\circ\) and \(75^\circ\).
\[
g = 180^\circ - 67^\circ - 75^\circ = 38^\circ
\]

Answers: \(f = 67^\circ\), \(g = 38^\circ\)

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Diagram 5:

- Given: \(124^\circ\)
- To find: \(h\) and \(i\)

Solution:
- The angle \(h\) is a corresponding angle to the given \(124^\circ\) angle.
\[
h = 124^\circ
\]
- The angle \(i\) is the angle inside the triangle. The sum of the angles in a triangle is \(180^\circ\). The other two angles in the triangle are \(90^\circ\) (right angle) and \(124^\circ - 90^\circ = 34^\circ\).
\[
i = 180^\circ - 90^\circ - 34^\circ = 56^\circ
\]

Answers: \(h = 124^\circ\), \(i = 56^\circ\)

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Diagram 6:

- Given: \(41^\circ\) and \(119^\circ\)
- To find: \(j\), \(k\), and \(l\)

Solution:
- The angle \(j\) is an alternate interior angle to the given \(41^\circ\) angle.
\[
j = 41^\circ
\]
- The angle \(k\) is a corresponding angle to the given \(119^\circ\) angle.
\[
k = 119^\circ
\]
- The angle \(l\) is the third angle in the triangle. The sum of the angles in a triangle is \(180^\circ\). The other two angles in the triangle are \(41^\circ\) and \(119^\circ\).
\[
l = 180^\circ - 41^\circ - 119^\circ = 20^\circ
\]

Answers: \(j = 41^\circ\), \(k = 119^\circ\), \(l = 20^\circ\)

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Final Answers:

\[
\boxed{
\begin{aligned}
& a = 51^\circ, \quad b = 104^\circ, \quad c = 117^\circ, \\
& d = 67^\circ, \quad e = 75^\circ, \quad f = 67^\circ, \quad g = 38^\circ, \\
& h = 124^\circ, \quad i = 56^\circ, \quad j = 41^\circ, \quad k = 119^\circ, \quad l = 20^\circ
\end{aligned}
}
\]