Question

2.Can you form a quadrilateral with the measures of the following angles.
a) 130°, 70°, 60°, 100°
b) 140°, 130, 50°, 60°
c) 80°, 90°, 120°, 70°
d) 160°, 90°, 80°, 70°
Please explain it properly Make this on your COPY It's urgent

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Answer 1

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The angles can form a quadrilateral are :

➙ a) 130°, 70°, 60°, 100°

➙ c) 80°, 90°, 120°, 70°

${{\underline{\underline{{\textsf{\textbf{Explanation : }}}}}}}$

We know that, a quadrilateral measures 360°

Here, four options with four angles are given where we need to find out the option which can form a quadrilateral.

Hence, In case of a) :

Given angles :

→ 130°, 70°, 60°, and 100°

Their sum must be 360°

→ 130 + 70 + 60 + 100

→ 360° ☑

Therefore, it can form a quadrilateral ☑

_____________________

Checking other options as well :

➪ b) 140°, 130°, 50°, 60°

→ 140° + 140° + 50° + 60°

→ 380°

• As it is not equal to 360°

It cannot form a quadrilateral.

________________

➪ c) 80°, 90°, 120°, 70°

→ 80 + 90 + 120 + 70

→ 360°

• It adds upto 360°

Therefore, it can form a quadrilateral ☑

_________________

➪ d) 160°, 90°, 80°, 70°,

→ 160 + 90 + 80 + 70

→ 400°

• As it is not equal to 360°

Therefore it can't form a quadrilateral.

_________________

Additional info :

• The sum of all angles in a quadrilateral is always 360° which is known as - the angle sum property of a quadrilateral.

Answer 2

To:-

See whether we can form a quadrilateral from the following angles.

Solution:-

a) 130°, 70°, 60°, 100°

We know that the sum all angles of a quadrilateral is always 360°

So let us find the sum of the given angles.

So,

130° + 70° + 60° + 100

= 200° + 160°

= 360°

Here the sum of all the angles of the quadrilateral is 360°

Hence, it is possible to make a quadrilateral from these angles.

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b) 140°, 130°, 50°, 60°

→ Let us find whether we can form a quadrilateral from the given angles using the same process.

Let us find the sum of all the angles.

So,

140° + 130° + 50° + 60°

= 270° + 110°

= 380°

Here we can see that the sum of all the given angles is greater than (or not equal to) 360°.

Hence,

It is not possible to make a quadrilateral from the given angles.

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c) 80°, 90°, 120°, 70°

→ Let us find the sum of all the given angles,

So,

80° + 90° + 120° + 70°

= 170° + 190°

= 360°

Here the sum of all the angles of a quadrilateral is 360°.

Hence, it is possible to form a quadrilateral from the given angles.

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d) 160°, 90°, 80°, 70°

→ Let us find the sum of all the given angles,

So,

160° + 90° + 80° + 70°

= 250° + 150°

= 400°

Here the sum of all the angles of the quadrilateral is greater than (or not equal to) 360°.

Hence it is not possible to form a quadrilateral from the given angles.

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Additional Information:-

Sum of all angles of a quadrilateral is always 360°. This property of the quadrilateral is known as angle - sum property of a quadrilateral.

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