Question

If the degree measures of the angles of the quadrilateral are 4x, 7x, 9x and 10x, What is the
measure of the smallest angle and the largest angle?
I will make you as brianlliest

Answer 1

Answer:

If the degree measures of the angles of the quadrilateral are 4x, 7x, 9x and 10x, What is the

measure of the smallest angle and the largest angle?

I will make you as brianlliest

Answer 2

Answer :-

• The smallest angle is 48°.
• The largest angle is 120°.

Given :-

• The degree measures of the angles of a quadrilateral are 4x, 7x, 9x and 10x.

To find :-

• The measure of the largest angle.
• The measure of the smallest angle.

Step-by-step explanation :-

• It has been given that the measures of the angles of a quadrilateral are 4x, 7x, 9x and 10x. We need to find the measure of the largest and the smallest angle. To find them, we first need to find the measure of all the angles, and then we can compare them to find our answer.

We know that :-

$\underline{\boxed{ \sf Sum \: of \: all \: angles \: of \: a \: quadrilateral = 360^{\circ}}}$

• So, all these angles must add up to 360°.

$\tt\implies 4x + 7x + 9x + 10x =360^{\circ}$

Adding 4x, 7x, 9x and 10x,

$\tt \implies 30x = 360^{\circ}$

Transposing 30 from LHS to RHS, changing it's sign,

$\tt\implies x = \dfrac{360^{\circ}}{30}$

Dividing 360° by 30,

$\underline{\boxed{\tt\implies x = 12^{\circ}.}}$

• The value of x is 12°.

Hence, all the angles are as follows :-

$\bf4x = 4 \times 12^{\circ} = 48^{\circ}.$

$\bf7x = 7 \times 12^{\circ} = 84^{\circ}.$

$\bf9x = 9 \times 12^{\circ} = 108^{\circ}.$

$\bf10x = 10 \times 12^{\circ} = 120^{\circ}$

As we can see,

$\boxed{\sf48^{\circ} \: is \: the \: smallest \: angle \: here.}$

$\boxed{\sf120^{\circ} \: is \: the \: largest \: angle \: here.}$

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• So, that means the smallest angle is 48° and the largest angle is 120°.