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Question
The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is ______.
Options
100°
150°
105°
120°
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Solution
The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is 150°.
Explanation:
Let EC and FC be altitudes and ∠ECF = 30°.
Let ∠EDC = x = ∠FBC
So, ∠ECD = 90° – x and ∠BCF = 90° – x
So, by property of the parallelogram,
∠ADC + ∠DCB = 180°
∠ADC + (∠ECD + ∠ECF + ∠BCF) = 180°
⇒ x + 90° – x + 30° + 90° – x = 180°
⇒ – x = 180° – 210° = – 30°
⇒ x = 30°
Hence, ∠DCB = 30° + 60° + 60° = 150°
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