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°

Answer 1

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°