The given information:
PS || QR (This means PS is parallel to QR)
∠PQR = 2x
∠QRS = 5x
∠RSP = 3x
When a transversal intersects two parallel lines, the alternate interior angles are equal.
In triangle QRS
∠QSR+∠QRS+∠RQS=180∘
3x + 5x + 2x = 180∘
10x = 180∘
x = 18∘
∠QRS = ∠QPS
∠QPS = 5x = 5 x 18° = 90°
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120 Mins English English20 Questions20 Marks15 Mins English English200 Questions200 Marks120 Mins EnglishPQ is a chord in the minor segment of a circle and R is a point on the minor arc PQ. The tangents at the points P and Q meet at the point T. If ∠PRQ =102°, then the measure of ∠PTQ is :
In △ABC, AB = AC = 12 cm, BC = 5 cm and D is a point on AC such that DB = BC. What is the measure of CD?
Which of the following statements is wrong ?
In the following table two columns are given. Match column A with column B.
Column A | Column B |
[a] Acute angle | [i] 90° |
[b] Obtuse angle | [ii] 240° |
[c] Right angle | [iii] 30° |
[d] Reflex angle | [iv] 120° |
How many lines of symmetry does the figure have?
Some statements are given about lines of symmetry.
(a) Equilateral triangle has 3 lines of symmetry.
(b) Circle has 2 lines of symmetry.
(c) An isosceles triangle has two lines of symmetry.
(d) A rectangle has two lines of symmetry.
(e) Letter A has one line of symmetry.
Which of the following option correctly describes all the above?
Which of the following statements is false?
A parallelogram is a quadrilateral in which:
In a quadrilateral ABCD, a line segment BD is a diagonal such that AB=CD and ∠ABD=∠CDB. Are the triangles ABD and CDB congruent? If so, by what rule?
A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. A second right-angled triangle is similar to the first, and its hypotenuse is 39 cm. What is the area of the second triangle?
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