Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find x + y + z
Two opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each angle of the parallelogram .
If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then find the measure of the smallest angle.
In a rhombus ABCD, if ∠ACB = 40°, then ∠ADB =
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 ______.
The sum of all ______ of a quadrilateral is 360°.
Sum of all the angles of a quadrilateral is 180°.
In a quadrilateral PQRS, ∠P = 50°, ∠Q = 50°, ∠R = 60°. Find ∠S. Is this quadrilateral convex or concave?
Three angles of a quadrilateral are equal. Fourth angle is of measure 120°. What is the measure of equal angles?
