Answer:
m∠d = 90°
m∠e = 129°
m∠f = 51°
Explanation:
Before attempting to calculate the values of the missing angles, first we must know a few properties about certain angles. Vertical angles are angles formed by two lines that cross and are opposite to each other, like the angle of 129° and ∠e for example, and they are equivalent to each other. Therefore, we know that the measure of ∠e, or m∠e, equals 129°.
Next, supplementary angles are two angles whose sums add up to exactly 180°, or a straight angle, and are typically adjacent angles formed on a straight line, like ∠e and ∠f. Since we know m∠e is 129°, and m∠e + m∠f = 180°, that means m∠f + 129 = 180 ⇒ m∠f = 51°.
Lastly, we also see that ∠d forms supplementary angles with a right angle - whose angle measure is 90° - so we can conclude that m∠d + 90 = 180 ⇒ m∠d = 90°.
Therefore, your answers will be: m∠d = 90°, m∠e = 129°, and m∠f = 51°.
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