Question

The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 55°. The largest angle of the parallelogram is ______.

Options

• 110°

• 125°

• 115°

• 130°

Answer 1

The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 55°. The largest angle of the parallelogram is 125°.

Explanation:

Let the obtuse angle at the vertex be x.

The acute angle between the two adjacent sides at that vertex is 180° – x.

The two altitudes through that vertex are perpendicular to those two sides. 

So, the acute angle between the altitudes equals the acute angle between the sides, i.e. 180° – x. 

Given 180° – x = 55°.

So, x = 180° – 55° = 125°.