Answer
Verified
439.8k+ views
Hint: We will be solving the question by individually checking the options provided to us. We will use the properties of angles such as
$\left( 1 \right)$ Sum of Supplementary angles is ${180^\circ }$.
$\left( 2 \right)$ Sum of all interior angles of a triangle is ${180^\circ }$.
$\left( 3 \right)$ Vertical angles are equal.
$\left( 4 \right)$ Corresponding angles are equal.
Complete step-by-step answer:
Let us add some more angles in the figure in order to understand better
Checking option \[\left( A \right)\quad {\left( {p + r} \right)^\circ }\]
As we can observe that
$\angle p + \angle m = {180^\circ }$ (Supplementary angles)
And $\angle m = \angle r$ (Corresponding angles)
$ \Rightarrow \angle p + \angle m = \angle p + \angle r = {180^\circ }$ (Since they are equal)
Checking option \[\left( B \right)\quad {\left( {p + t} \right)^\circ }\]
We can see that from the data given we cannot conclude that the value of \[{\left( {p + t} \right)^\circ } = {180^\circ }\].
Therefore, we will check other options.
Checking option \[\left( C \right)\quad {\left( {q + s} \right)^\circ }\]
As we can observe that
$\angle q + \angle n = {180^\circ }$ (Supplementary angles)
And $\angle n = \angle s$ (Corresponding angles)
$ \Rightarrow \angle q + \angle n = \angle q + \angle s = {180^\circ }$ (Since they are equal)
Checking option \[\left( D \right)\quad {\left( {r + s + t} \right)^\circ }\]
As we can observe from the figure
$
\angle r = \angle x \\
\angle s = \angle y \\
\angle t = \angle z \\
$(Vertical angles)
In addition, we know that sum of all interior angles of a triangle $ = {180^\circ }$.Therefore,
$
\Rightarrow \angle x + \angle y + \angle z = {180^\circ } \\
\Rightarrow \angle r + \angle s + \angle t = {180^\circ } \\
$
Therefore \[{\left( {r + s + t} \right)^\circ } = 180^\circ \]
Checking option \[\left( E \right)\quad {\left( {t + u} \right)^\circ }\]
We can see that $\angle t$ and $\angle u$ are supplementary angles. Therefore,
$ \Rightarrow \angle t + \angle u = 180^\circ $
After checking all the options, we can Conclude that the options $\left( A \right),\left( C \right),\left( D \right),\left( E \right)$ are all equal to ${180^\circ }$. So by eliminating these options, we are only left with option $\left( B \right)$
Hence, the correct answer is $\left( B \right)$.
Note: It should be noted that the angles $r,s\;and\;t$ are not the exterior angles of the triangle formed. Therefore, you cannot apply “the sum of exterior angles of a convex polygon is ${360^0}$” property.
$\left( 1 \right)$ Sum of Supplementary angles is ${180^\circ }$.
$\left( 2 \right)$ Sum of all interior angles of a triangle is ${180^\circ }$.
$\left( 3 \right)$ Vertical angles are equal.
$\left( 4 \right)$ Corresponding angles are equal.
Complete step-by-step answer:
Let us add some more angles in the figure in order to understand better
Checking option \[\left( A \right)\quad {\left( {p + r} \right)^\circ }\]
As we can observe that
$\angle p + \angle m = {180^\circ }$ (Supplementary angles)
And $\angle m = \angle r$ (Corresponding angles)
$ \Rightarrow \angle p + \angle m = \angle p + \angle r = {180^\circ }$ (Since they are equal)
Checking option \[\left( B \right)\quad {\left( {p + t} \right)^\circ }\]
We can see that from the data given we cannot conclude that the value of \[{\left( {p + t} \right)^\circ } = {180^\circ }\].
Therefore, we will check other options.
Checking option \[\left( C \right)\quad {\left( {q + s} \right)^\circ }\]
As we can observe that
$\angle q + \angle n = {180^\circ }$ (Supplementary angles)
And $\angle n = \angle s$ (Corresponding angles)
$ \Rightarrow \angle q + \angle n = \angle q + \angle s = {180^\circ }$ (Since they are equal)
Checking option \[\left( D \right)\quad {\left( {r + s + t} \right)^\circ }\]
As we can observe from the figure
$
\angle r = \angle x \\
\angle s = \angle y \\
\angle t = \angle z \\
$(Vertical angles)
In addition, we know that sum of all interior angles of a triangle $ = {180^\circ }$.Therefore,
$
\Rightarrow \angle x + \angle y + \angle z = {180^\circ } \\
\Rightarrow \angle r + \angle s + \angle t = {180^\circ } \\
$
Therefore \[{\left( {r + s + t} \right)^\circ } = 180^\circ \]
Checking option \[\left( E \right)\quad {\left( {t + u} \right)^\circ }\]
We can see that $\angle t$ and $\angle u$ are supplementary angles. Therefore,
$ \Rightarrow \angle t + \angle u = 180^\circ $
After checking all the options, we can Conclude that the options $\left( A \right),\left( C \right),\left( D \right),\left( E \right)$ are all equal to ${180^\circ }$. So by eliminating these options, we are only left with option $\left( B \right)$
Hence, the correct answer is $\left( B \right)$.
Note: It should be noted that the angles $r,s\;and\;t$ are not the exterior angles of the triangle formed. Therefore, you cannot apply “the sum of exterior angles of a convex polygon is ${360^0}$” property.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
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
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE