Question

DATE
are
Two adjacent angles of a rhombus are in the ratio 3:7 what will be the smallest measure is​

Answer 1

Answer:-

Given:

Adjacent angles of a rhombus are in the ratio 3 : 7.

We know that,

Sum of measures of adjacent angles of a rhombus = 180°

So, let the measures of the angles be 3x , 7x.

Hence,

→ 3x + 7x = 180°

→ 10x = 180°

→ x = 180/10

→ x = 18

Hence,

• 1st angle = 3x = 3(18) = 54°

• 2nd angle = 7x = 7(18) = 126°

We know that,

The measures of Opposite angles of a rhombus are equal.

So, the measures of other two angles are also 54° , 126°.

On comparing the measures of four angles we can say that angle with smallest measure is 54°.

Answer 2

Given:

• The adjacent angles of rhombus are in the ratio 3:7

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Need to find:

• The measure of each angle=?

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Solution:

Let the angles be:

• 7x and
• 3x

We know

The sum of adjacent angles of a rhombus is 180°.

Thus,

7x+ 3x= 180°

→ 10x= 180°

→ x= 18°

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The angles are:

■ 3x

= 3× 18°

=54°

And

■7x

=7× 18°

=126°

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Now. The opposite angles of a rhombus are equal thus the angles are:

$\blue{54\degree\:, 126\degree\:, 54\degree\:, 126\degree\:}$

$\therefore$ The smallest angle measures $\red{\bold{\boxed{54\degree}}}$