In the adjoining figure, ABCD is a square. A line segment CX cuts AB a

1.	In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD at O such that ∠ COD = 80° and ∠ OXA = x°. Find the value of x.
Answer» In △ ABD We know that AB = AD From the figure we know that the base angles are equal ∠ ADB = ∠ ABD We know that ∠ A = 90^o It can be written as ∠ ADB + ∠ ABD = 90^o We know that ∠ ADB = ∠ ABD So we get 2 ∠ ADB = 90^o By division ∠ ADB = 45^o Consider △ OXB From the figure we know that ∠ XOB and ∠ DOC are vertically opposite angles ∠ XOB = ∠ DOC = 80^o We also know that ∠ ABD = ∠ XBD = 45^o We can write it as Exterior ∠ AXO = ∠ XOB + ∠ XBD By substituting the values x^o = 80^o + 45^o By addition x^o = 125^o Therefore, the value of x is 125^o.

In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD at O such that ∠ COD = 80° and ∠ OXA = x°. Find the value of x.

Answer»

In △ ABD

We know that AB = AD

From the figure we know that the base angles are equal

∠ ADB = ∠ ABD

We know that ∠ A = 90^o

It can be written as

∠ ADB + ∠ ABD = 90^o

We know that ∠ ADB = ∠ ABD

So we get

2 ∠ ADB = 90^o

By division

∠ ADB = 45^o

Consider △ OXB

From the figure we know that ∠ XOB and ∠ DOC are vertically opposite angles

∠ XOB = ∠ DOC = 80^o

We also know that

∠ ABD = ∠ XBD = 45^o

We can write it as

Exterior ∠ AXO = ∠ XOB + ∠ XBD

By substituting the values

x^o = 80^o + 45^o

By addition

x^o = 125^o

Therefore, the value of x is 125^o.

Discussion

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