Question

Can someone help me with this problem please

Answer 1

The correct option is third one m∠2 =106° , m∠3 =37°.

Therefore,

`m\angle 2 = 106\°\\m\angle 3 = 37\°`

Explanation:

Given:

Consider ABCD as a Rhombus such that,

∠A = ∠1 = 106°

∠C = ∠2

∠BDC = ∠3

AB=BC=CD=DA

To Find:

∠2 = ?

∠3 = ?

Solution:

ABCD is a Rhombus

∠A ≅ ∠C ............opposite angles of Rhombus are equal. ( property )

Substituting the values we get

∠1 = ∠2

But ∠1 = 106°

∴ ∠2 = 106° ....... Transitive property,

As BC = CD ...Given

ΔBCD is an Isosceles triangle

∴ ∠CBD ≅ ∠BDC = ∠3 ........base angle of Isosceles triangle are congruent.

we know that in a triangle,

Sum of measures of all angles is 180°

in Triangle BCD

`\angle 3 +\angle 2 +\angle 3 =180`

Substituting the values we get

`2m\angle 3 =180-106=74\\\\\angle 3=(74)/(2)=37\\\\m\angle 3 = 37\°`

Therefore,

`m\angle 2 = 106\°\\m\angle 3 = 37\°`