Problem: Vertically Opposite Angles (Part 1)
The task is to find the size of the missing angles in each diagram. The key concept here is that
vertically opposite angles are equal. Additionally, since AB and CD are straight lines, the angles on a straight line sum up to
180°.
Let's solve each part step by step:
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(a)
- Given: \( \angle x = 65^\circ \)
- To find: \( \angle y \)
Solution:
- Vertically opposite angles are equal.
- Therefore, \( \angle y = \angle x = 65^\circ \).
Answer: \( \angle y = 65^\circ \)
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####
(b)
- Given: \( \angle x = 70^\circ \)
- To find: \( \angle z \)
Solution:
- Vertically opposite angles are equal.
- Therefore, \( \angle z = \angle x = 70^\circ \).
Answer: \( \angle z = 70^\circ \)
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(c)
- Given: \( \angle z = 155^\circ \)
- To find: \( \angle z \) (redundant, but we need to confirm consistency)
Solution:
- Vertically opposite angles are equal.
- Therefore, \( \angle z = 155^\circ \) (as given).
Answer: \( \angle z = 155^\circ \)
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(d)
- Given: \( \angle x = 125^\circ \)
- To find: \( \angle y \)
Solution:
- Vertically opposite angles are equal.
- Therefore, \( \angle y = \angle x = 125^\circ \).
Answer: \( \angle y = 125^\circ \)
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(e)
- Given: \( \angle x = 100^\circ \)
- To find: \( \angle z \)
Solution:
- Vertically opposite angles are equal.
- Therefore, \( \angle z = \angle x = 100^\circ \).
Answer: \( \angle z = 100^\circ \)
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####
(f)
- Given: \( \angle x = 160^\circ \)
- To find: \( \angle z \)
Solution:
- Vertically opposite angles are equal.
- Therefore, \( \angle z = \angle x = 160^\circ \).
Answer: \( \angle z = 160^\circ \)
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Final Answers:
\[
\boxed{
\begin{aligned}
&\text{(a)} \; \angle y = 65^\circ \\
&\text{(b)} \; \angle z = 70^\circ \\
&\text{(c)} \; \angle z = 155^\circ \\
&\text{(d)} \; \angle y = 125^\circ \\
&\text{(e)} \; \angle z = 100^\circ \\
&\text{(f)} \; \angle z = 160^\circ
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of find vertical angles worksheet.
