Advertisements
Advertisements
Question
ABCD is a parallelogram. Find the value of x, y and z.
Advertisements
Solution
Given, A parallelogram ABCD.
In the ΔOBC, we have
y + 30° = 100° ...[Exterior angle property of triangle]
⇒ y = 70°
By the angle sum property of a triangle,
We have, x + y + 30° = 180°
⇒ x + 70° + 30° = 180°
⇒ x = 180° – 100°
⇒ x = 80°
Now, since AD || BC and BD is transversal,
Therefore, ∠ADO = ∠OBC ...[Alternative interior angles]
⇒ z = 30°
APPEARS IN
RELATED QUESTIONS
Consider the given parallelograms. Find the values of the unknowns x, y, z.
If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.
In the given figure, `square`ABCD is a parallelogram. Point E is on the ray AB such that BE = AB then prove that line ED bisects seg BC at point F.
In parallelogram PQRS, ∠Q = (4x – 5)° and ∠S = (3x + 10)°. Calculate: ∠Q and ∠R.
Prove that the diagonals of a parallelogram bisect each other.
In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.
Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between c and f
If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)°, then the ratio of these angles is ______.
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45°. Find the angles of the parallelogram.
