Adjacent Angles Worksheets - 15 Worksheets Library - Free Printable

Problem Analysis:

The worksheet focuses on adjacent angles, which are defined as a pair of angles that share a common vertex and a common arm but do not overlap. The task involves identifying adjacent angles, determining whether given angle pairs are adjacent, and identifying the common arm for adjacent angles.

Let's solve each section step by step:

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Section A: Identify the two pairs of adjacent angles in each figure

#### 1)
- Figure: Two intersecting lines forming four angles.
- Angles: \(a\), \(b\), \(c\), and another angle (not labeled).
- Adjacent Pairs:
- \(a\) and \(b\) share a common vertex and a common arm.
- \(b\) and \(c\) share a common vertex and a common arm.
- Answer: \((a, b)\) and \((b, c)\).

#### 2)
- Figure: Two intersecting lines forming four angles.
- Angles: \(d\), \(e\), \(f\), and another angle (not labeled).
- Adjacent Pairs:
- \(d\) and \(e\) share a common vertex and a common arm.
- \(e\) and \(f\) share a common vertex and a common arm.
- Answer: \((d, e)\) and \((e, f)\).

#### 3)
- Figure: Two intersecting lines forming four angles.
- Angles: \(g\), \(h\), \(i\), and another angle (not labeled).
- Adjacent Pairs:
- \(g\) and \(h\) share a common vertex and a common arm.
- \(h\) and \(i\) share a common vertex and a common arm.
- Answer: \((g, h)\) and \((h, i)\).

#### 4)
- Figure: Two intersecting lines forming four angles.
- Angles: \(j\), \(k\), \(l\), and another angle (not labeled).
- Adjacent Pairs:
- \(j\) and \(k\) share a common vertex and a common arm.
- \(k\) and \(l\) share a common vertex and a common arm.
- Answer: \((j, k)\) and \((k, l)\).

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Section B: State whether the indicated angle pairs are adjacent or not

#### 1)
- Figure: Two angles \(x\) and \(y\) sharing a common vertex and a common arm.
- Analysis: \(x\) and \(y\) share a common vertex and a common arm, and they do not overlap.
- Answer: Adjacent.

#### 2)
- Figure: Two angles \(m\) and \(n\) not sharing a common arm.
- Analysis: \(m\) and \(n\) do not share a common arm.
- Answer: Not adjacent.

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Section C: Identify the arm common to adjacent angles in each figure

#### 1)
- Figure: Two angles \(c\) and \(d\) sharing a common vertex and a common arm.
- Common Arm: The ray extending from the vertex through the point where both angles meet.
- Answer: The ray common to both angles \(c\) and \(d\).

#### 2)
- Figure: Two angles \(p\) and \(q\) sharing a common vertex and a common arm.
- Common Arm: The ray extending from the vertex through the point where both angles meet.
- Answer: The ray common to both angles \(p\) and \(q\).

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Final Answers:

Section A:
1. \((a, b)\) and \((b, c)\)
2. \((d, e)\) and \((e, f)\)
3. \((g, h)\) and \((h, i)\)
4. \((j, k)\) and \((k, l)\)

Section B:
1. Adjacent
2. Not adjacent

Section C:
1. The ray common to both angles \(c\) and \(d\).
2. The ray common to both angles \(p\) and \(q\).

Boxed Final Answer:
\[
\boxed{
\text{A: } (a, b), (b, c); (d, e), (e, f); (g, h), (h, i); (j, k), (k, l) \\
\text{B: } \text{Adjacent; Not adjacent} \\
\text{C: } \text{Common ray for } c \text{ and } d; \text{Common ray for } p \text{ and } q
}
\]