Answer

Verified

439.8k+ views

**Hint:**Two Angles are Supplementary when they add up to \[{180^ \circ }\]. The two angles (\[{140^ \circ }\]and \[{40^ \circ }\]) are Supplementary Angles, because they add up to \[{180^ \circ }\]. Notice that together they make a straight angle. When the sum of two angles is \[{180^ \circ }\], then the angles are known as supplementary angles. In other words, if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles. These two angles form a linear angle, where if one angle is x, then the other the angle is \[\left( {180 - x} \right)\].

**Complete step by step solution:**In geometry, there are many types of angles with many different measures. Some angles are related to other angles because of how their measures are related. This is the case with supplementary angles, and we have a nice rule to help us understand the definition of the supplement of an angle.The supplement of an angle, is another angle, such that the sum of the measure of first angle and the measure of second angle is equal to \[{180^ \circ }\]

Let the angle be \[x\]

Therefore, its supplementary angle would be \[\left( {180 - x} \right)\]

According to the question,

\[x = \dfrac{1}{5}{\text{ }} \times \left( {180 - x} \right)\]

After Cross multiplying, we get

\[6x = 180\]

Divide both sides by \[6\], we get

\[\begin{gathered}

x = \dfrac{{180}}{6} \\

x = 30 \\

\end{gathered} \]

Therefore, the angle will be \[{30^ \circ }\]. So the answer of this question will be \[{30^ \circ }\]

**Note:**When the two angles add to \[{180^ \circ }\], we say they "Supplement" each other. Supplement comes from Latin supplier, to complete or "supply" what is needed

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference Between Plant Cell and Animal Cell