Question

find the measure of the missing angles.
answer attempt 1 out of 2
$d = square ^ { circ }$
$e = square ^ { circ }$
$f = square ^ { circ }$
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Explanation:

Step1: Find \(d\)

Vertical angles are equal. \(d = 103^{\circ}\) (vertical angles with \(103^{\circ}\))

Step2: Find \(e\)

\(46^{\circ}\) and \(e\) are vertical angles. So \(e = 46^{\circ}\)

Step3: Find \(f\)

The sum of angles around a point is \(360^{\circ}\). But we can also use the fact that adjacent angles on a straight - line sum to \(180^{\circ}\).
\(46^{\circ}+103^{\circ}+f = 180^{\circ}\) (angles on a straight - line)
\(f=180^{\circ}-(46^{\circ} + 103^{\circ})\)
\(f = 31^{\circ}\)

Answer:

\(d = 103^{\circ}\), \(e = 46^{\circ}\), \(f = 31^{\circ}\)