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# The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60º. Find the angles of the parallelogram.

**Solution:**

Given, the angle between two altitudes of a __parallelogram__ through the vertex of an __obtuse angle__ of the parallelogram is 60º

We have to find the angles of the parallelogram.

Consider a parallelogram ABCD

∠ADC and ∠ABC are the two obtuse angles of the parallelogram

DQ and DP are the two altitudes of the parallelogram

DP ⊥ AB

DQ ⊥ BC.

∠PDQ = 60

In quadrilateral DPBQ,

We know that according to the __quadrilateral__ angle sum property, the sum of all the four interior angles is 360 degrees.

Sum of all __interior angles__ of a quadrilateral is = 360º

We have,

∠PDQ + ∠Q + ∠P + ∠B = 360º

60 + 90 + 90 + ∠B = 360º

240 + ∠B = 360º

∠B = 360º - 240º

∠B = 120º

Since, opposite angles in parallelogram are equal,

∠B = ∠D = 120º

Since, opposite sides are parallel in parallelogram,

AB||CD

Also, since sum of adjacent interior angles is 180 degrees

∠B + ∠C = 180º

120 + ∠C = 180º

∠C = 180º - 120º

∠C = 60º

Since, opposite angles in parallelogram are equal,

∠C = ∠A = 60º

Therefore, areas of the parallelogram are 60º, 120º, 60º and 120º

**✦ Try This: **The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45º. Find the angles of the parallelogram.

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.3 Problem 3**

## The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60º. Find the angles of the parallelogram.

**Summary:**

The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60º. The angles of the parallelogram are 60º, 120º, 60º and 120º

**☛ Related Questions:**

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