Question

B
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 ZOXA X". Find the value of x.
80
A
In the adjoin figure, AL and CM are perpendicular to diagonal BD of al gm ABCD. Prove
that (i) AALD ACMB, (ii) AL CM​

Answer 1

Question

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 x= 55°

Solution

Given

• ABCD is a Square.
• DOC = 80⁰
• DB is a Diagonal.

To Find

• The Value Of x

→ DOX = 180 - COD

→ DOX = 180 - 80⁰

→ DOX= 100⁰

Now In ∆ XOB We have,

• ∠XBO = 45 °. "The diagonals of a square bisect the vertex angle."
• ∠XOB = ∠DOC Vertically Opposite Angle

We know That,

• ∠OXB+∠OBX+∠XOB= 180 ∠angle Sum Property

∠OXB= 180-80-45

• ∠OXB= 55°

Now In the Given Figure

∠x= 180-∠OXB

∠x = 180- 55°

• ∠x = 125°