Advertisements
Advertisements
Question
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.
Advertisements
Solution
In quadrilateral DPBQ:
∠1 + ∠2 + ∠B + ∠3 = 360° ...[Angle sum property of quadrilateral]
60° + 90° + ∠B + 90° = 360°
∠B + 240° = 360°
∠B = 360° – 240°
∠B = 120°
Since, ∠ADC = ∠B = 120° ...[Opposite angles of a parallelogram are equal]
∠A + ∠B = 180° ...[Sum of consecutive interior angle is 180°]
∠A + 120° = 180°
∠A = 180° – 120°
∠A = 60°
So, ∠C = ∠A = 60° ...[Opposite angle of a parallelogram are equal]
APPEARS IN
RELATED QUESTIONS
Find x + y + z + w
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13 Find all the angles of the quadrilateral.
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram .
ABCD is a parallelogram in which ∠A = 70°. Compute ∠B, ∠C and ∠D .
If PQRS is a square, then write the measure of ∠SRP.
Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.
One angle of a quadrilateral is of 108º and the remaining three angles are equal. Find each of the three equal angles.
A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is ______.
Which of the following can be four interior angles of a quadrilateral?
Sum of all the angles of a quadrilateral is 180°.
