Geometry (Part-5)

Total Questions: 50

21. For triangles, which of the following statement(s) are true? [SSC CGL 26/09/2024 (1st Shift)]

(a) Sum of interior angles is 180°.
(b) All interior angles can't be equal.
(c) Can have at the most one obtuse angle.
(d) Sum of two sides may or may not be equal to the third side.

Correct Answer: (d) (a) and (c)
Solution:both (a) and (c) are correct. A triangle can have at most one obtuse angle and sum of all interior angles is always 180º.

22. If the angles of a triangle are in the ratio 7 : 8 : 3, then the value of the largest angle is: [SSC CGL 26/09/2024 (1st Shift)]

Correct Answer: (b) 80º
Solution:

23. Explain it- [SSC CGL 26/09/2024 (1st Shift)]

Correct Answer: (a) 7,850
Solution:

24. The side BC of ∆ABC is produced to a point D. If AC = BC and ∠BAC = 70º then find the value of 2.5∠ACD - 1.5∠ABC. [SSC CGL 26/09/2024 (2nd Shift)]

Correct Answer: (a) 245º
Solution:

25. In ∆ABC, DE || BC and 5AE = 3EC If AB = 6.4 units, then the value of DB (in units) is: [SSC CGL 26/09/2024 (2nd Shift)]

Correct Answer: (d) 4
Solution:

26. In a circle with center O, an arc ABC subtends an angle of 138° at the centre of the circle. The chord AB is produced to a point P. Then, the measure of ∠CBP is: [SSC CGL 26/09/2024 (2nd Shift)]

Correct Answer: (d) 69°
Solution:

27. If the altitude from two vertices of a triangle to the opposite sides are equal, then the triangle will be: [SSC CGL 26/09/2024 (3rd Shift)]

Correct Answer: (a) isosceles triangle
Solution:

Isosceles triangle
If 2 altitudes of a triangle are equal then the triangle formed is an isosceles triangle.

28. In a triangle PQR, ∠P + ∠Q = 84°. Find the value of ∠R. [SSC CGL 26/09/2024 (3rd Shift)]

Correct Answer: (b) 96°
Solution:

∠P + ∠Q + ∠R = 180º
∠R = 180º - 84º = 96º

29. In triangle XYZ, A is a point on YZ such that XA = YA. If ∠XYA = 50° and ∠AXZ = 19°, what is the degree measure of ∠XZA. [SSC CGL 26/09/2024 (3rd Shift)]

Correct Answer: (a) 61°
Solution:

30. Given that the perimeters of two similar triangles, ∆ABC and ∆DEF, are 24 cm and 9 cm, respectively, and DE = 3 cm, what is the ratio between the area of ∆ABC and that of ∆DEF? [SSC CHSL 01/07/2024 (1st Shift)]

Correct Answer: (c) 64 : 9
Solution: