Question

2) In the figure, ABCD is a rhombus, whose diagonals meet at O and
mzA=35°. Find the values of x and y.
a) x= 55°,y=125°
b) x=55°,y=55° c) x=35°,y=35°
d) x=125°,y=55°​

Answer 1

Answer:

Option(b)=x=55° , y=55°

Step-by-step explanation:

In quad. ABCD,

<AOB=90°......... Diagonals of rhombus bisect each other at 90°

In tri. AOB,

<AOB+<OAB+<OBA=180°....... Angle sum property of triangle

90°+35°+x=180°

125°+x=180°

x=180°-125°

x=55°

In triangle ADB,

AD=AB........sides of rhombus

Therefore triangle ADB is isosceles

<ADB=<ABD

y=x

y=55°

Therefore option(b) is correct!!

Hope it helps you!!

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Answer 2

Given:

• ABCD is a rhombus
• ∠A = 35°

To Find:

• The values of x and y.

Solution:

Consider ΔAOB,

⇒ ∠AOB = 90° ( Diagonals of a rhombus bisect each other at an angle of 90°)

We know that the addition of all the three angles of a triangle is 180° ( Angle sum property of a triangle)

∴ ∠AOB+∠OAB+∠ABO = 180°

⇒ 90°+35°+∠ABO = 180°

⇒ 125°+∠ABO = 180°  ( rearranging the equation to get the value of ∠ABO)

⇒ ∠ABO = 180° - 125° = 55°

⇒ x = 55°

Consider Δ ADB,

We know that the sides of a rhombus are equal, therefore, side AD will be equal to side AB.

∴ AD = AB

⇒ Triangle ADB is an isosceles triangle.

In an isosceles triangle, two sides and two angles of the triangle are equal.

∴ angle x = angle y

∴ ∠y = ∠x = 55°

∴ The value of x is the same as y which is equal to 55°. (option b)