Math, asked by sp15051979, 5 months ago

find the measures of the numbered angle in each rhombus

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Answered by snehaprajnaindia204

Answer:

Answered by kmousmi293

Answer:

The measurements of all the required angles of the rhombus are ∠1 = 124°, ∠2 = 28°, ∠3 = 28°, ∠4 = 124°, and ∠5 = 28°.

Step-by-step explanation:

A rhombus has been given measurements of some of its angles,

So, we have;

∠2 = 28° ( equal sides of a rhombus)

Applying the angle sum property in the triangle, we get

28° + ∠2 + ∠1 = 180°

Applying ∠2 = 28° in the above equation, we have;

28° + 28° + ∠1 = 180°

∠1 = 180° - ( 28° + 28° )

∠1 = 180° - 56° = 124°

Now, we know that the diagonals of a rhombus bisect the angle,

So, ∠5 = 28° and ∠3 = ∠2 = 28°

Again applying the angle sum property, according to which the sum of all angles of a triangle is 180°.

We have,

∠3 + ∠4 + ∠5 = 180°

So, ∠4 = 124°.

Therefore, the measurements of all the required angles of the rhombus are ∠1 = 124°, ∠2 = 28°, ∠3 = 28°, ∠4 = 124°, and ∠5 = 28°.

To read more about rhombus, visit

https://brainly.in/question/15117702

https://brainly.in/question/2879974

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