Exercise 2

Chapter 2, Section 2-1, Page 72
enVision Geometry 1st Edition by Al Cuoco
ISBN: 9780328931583

Solution

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4\angle 4 forms a linear pair with 1\angle 1 and with 3\angle 3 so they are supplementary:

1+4=180°\angle 1+\angle 4=180\text{\textdegree}

1+118°=180°\angle 1+118\text{\textdegree}=180\text{\textdegree}

1=62°\color{#c34632}{\angle 1 =62\text{\textdegree}}

3+4=180°\angle 3+\angle 4=180\text{\textdegree}

3+118°=180°\angle 3+118\text{\textdegree}=180\text{\textdegree}

3=62°\color{#c34632}{\angle 3 =62\text{\textdegree}}

4\angle 4 and 2\angle 2 are vertical angles so they are congruent. Hence, their measures are equal:

2=4\angle 2 =\angle 4

2=118°\color{#c34632}{\angle 2 =118\text{\textdegree}}

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