Question

1. use the drawing at the right to answer the following questions. a) what is ( mangle boa )? b) name an angle that is adjacent to ( angle doc ). c) name two angles that are vertical angles. d) name two angles that make up a linear pair. e) name three points that are collinear. f) what point is in the interior of ( angle eod )?

Explanation:

Step1: Find \(m\angle BOA\)

Since \(\angle EOA = 90^{\circ}\) (right angle) and \(\angle EOF=52^{\circ}\), and \(\angle BOA\) and \(\angle EOF\) are vertical angles. Vertical angles are equal.
\(m\angle BOA = 52^{\circ}\)

Step2: Name an angle adjacent to \(\angle DOC\)

Adjacent angles share a common side and a common vertex. \(\angle BOC\) shares side \(OC\) and vertex \(O\) with \(\angle DOC\)

Step3: Name two angles that are vertical angles

Vertical angles are opposite angles formed by the intersection of two lines. \(\angle EOF\) and \(\angle BOA\) are vertical angles, \(\angle EOD\) and \(\angle AOC\) are vertical angles

Step4: Name two angles that make up a linear pair

A linear pair of angles is adjacent and supplementary (sum to \(180^{\circ}\)). \(\angle EOD\) and \(\angle EOC\) form a linear pair (\(\angle EOD+\angle EOC = 180^{\circ}\))

Step5: Name three points that are collinear

Collinear points lie on the same straight line. Points \(D\), \(O\), \(A\) lie on a straight line

Step6: Find a point in the interior of \(\angle EOD\)

The interior of an angle is the region between the two sides of the angle. Point \(F\) is in the interior of \(\angle EOD\)

Answer:

a) \(m\angle BOA = 52^{\circ}\)
b) \(\angle BOC\) (one possible answer for adjacent to \(\angle DOC\))
c) \(\angle EOF\) and \(\angle BOA\), \(\angle EOD\) and \(\angle AOC\) (vertical angles)
d) \(\angle EOD\) and \(\angle EOC\) (linear - pair example)
e) \(D\), \(O\), \(A\) (collinear points example)
f) \(F\) (point in the interior of \(\angle EOD\))