Advertisements
Advertisements
Question
In a quadrilateral PQRS, ∠P = 50°, ∠Q = 50°, ∠R = 60°. Find ∠S. Is this quadrilateral convex or concave?
Advertisements
Solution
Given a quadrilateral PQRS,
Where ∠P = 50°, ∠Q = 50° and ∠R = 60°
Now, by the angle sum property of a quadrilateral, we have
∠P + ∠Q + ∠R + ∠S = 360°
⇒ 50° + 50° + 60° + ∠S = 360°
⇒ ∠S = 360° – 160°
⇒ ∠S = 200°
Since, one interior angle of the given quadrilateral is obtuse, therefore the quadrilateral is concave.
APPEARS IN
RELATED QUESTIONS
Find the angle measure x in the given Figure
In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angles of the quadrilateral
Two opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each angle of the parallelogram .
In Fig. below, ABCD is a parallelogram in which ∠DAB = 75° and ∠DBC = 60°. Compute
∠CDB and ∠ADB.
If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then find the measure of the smallest angle.
In the given figure, PQRS is a rhombus in which the diagonal PR is produced to T. If ∠SRT = 152°, find x, y and z.
The figure formed by joining the mid-points of the adjacent sides of a square is a
Can all the angles of a quadrilateral be acute angles? Give reason for your answer.
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.
The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a ______.
