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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150 Mins English English150 Questions150 Marks150 Mins English English150 Questions150 Marks150 Mins EnglishIn △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?
PQ 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 :
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 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?
The length of each of two tangents drawn from an external point to a circle is 10 cm. What is the approximate distance from the external point to the center of the circle, if the radius is 6 cm?
A circle is inscribed in a right triangle with legs of length 5 and 12. What is the radius of the circle?
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