Q13 of 109 Page 300

In the adjoining figures, is a square. A line segment cuts at and the diagonal at such that and Find the value of

Here, ABCD is square.


Here AC and BD are diagonals.


We know that the angles of a square are bisected by the diagonals.


∴ ∠​OBX = 45° ∵∠​ABC = 90° and BD bisects ∠​ABC​
And ∠​BOX = ∠COD = 80° … Vertically opposite angles
∴​ In ∆BOX, we have:
∠AXO = ∠OBX + ​∠BOX … Exterior angle theorem
⇒​ ∠AXO = 45° + 80° = 125°
∴ ​x =125°


More from this chapter

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11

Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. Find the length of the other diagonal and hence find the area of the rhombus.

 12

In each of the figures given below, is a rectangle. Find the values of and in each case.

 14

In the adjoining figures, and are perpendiculars to the diagonal of a ||gm Prove that

(i) (ii)


15

In the adjoining figures, is a parallelogram in which the bisectors of and intersect at a point Prove that