Mathematics

In the figure $$\angle P + \angle Q + \angle R + \angle S + \angle T = 2$$ right angles


ANSWER

True


SOLUTION
Sum of angles on a straight line=$${ 180 }^{ \circ  }$$
$$\implies\quad \angle PAE={ 180 }^{ \circ  }-\angle 1$$
$$ Similarly,\angle PEA={ 180 }^{ \circ  }-\angle 5$$
$$ In\triangle PAE$$
$$ \angle PAE+\angle PEA+\angle APE={ 180 }^{ \circ  }$$
$$\implies\quad 180-\angle 1+180-\angle 5+\angle APE={ 180 }^{ \circ  }$$
$$\implies\quad \angle APE=\angle 1+\angle 5-{ 180 }^{ \circ  }=\angle P$$
$$ Similarly,\angle BSC=\angle 2+\angle 3-{ 180 }^{ \circ  }=\angle S$$
$$ \angle DRC=\angle 3+\angle 4-{ 180 }^{ \circ  }=\angle R$$
$$ \angle DQE=\angle 4+\angle \angle 5-{ 180 }^{ \circ  }=\angle Q$$
$$ \angle ATS=\angle 1+\angle 2-{ 180 }^{ \circ  }=\angle T$$
$$\implies\quad \angle P+\angle Q+\angle R+\angle S+\angle T$$
$$ =\angle 1+\angle 2+\angle 3+\angle 4+\angle 2+\angle 3+\angle 4+\angle 5+\angle 1+\angle 5-(180\times 5)$$
$$ =2(\angle 1+\angle 2+\angle 3+\angle 4+\angle 5)-900\quad -(1)$$
From pentagon ABCDE,
Sum of angles of pentagon=$$((2\times 5)-4)\times { 90 }^{ \circ  }$$
($$\because$$ Sum of angles=$$(2n-4)\times { 90 }^{ \circ  }$$)
$$=6\times 90={ 540 }^{ \circ  }$$
$$\implies\quad \angle P+\angle Q+\angle R+\angle S+\angle T=2({ 540 }^{ \circ  })-{ 900 }^{ \circ  }$$
$$ ={ 1080 }^{ \circ  }-{ 900 }^{ \circ  }$$
$$ ={ 180 }^{ \circ  }$$
$$ =2\times 90$$
$$ =2\quad Right\quad angles$$
$$A)True$$
View Answers

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


TRUE/FALSE Medium Published on 09th 09, 2020
Next Question
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 85
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
In the given figure OA, OB are opposite rays and $$\angle AOC+\angle BOD =90^{\circ}$$, then $$\angle COD$$ is
  • A. $$60^{\circ}$$
  • B. $$45^{\circ}$$
  • C. $$30^{\circ}$$
  • D. $$90^{\circ}$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q2 One Word Medium
Two lines AB and CD intersect at O. If $$ \angle AOC+\angle COB+ \angle BOD = 270^{\circ}, $$ find the measures of $$ \angle AOC,\angle COB,\angle BOD $$ and $$ \angle DOA.$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q3 Single Correct Medium
If O is the ethnocentric of the $$\Delta ABC$$, then
  • A. $$\angle BOC = 2\angle BAC$$
  • B. $$\angle BOC = \angle BAC$$
  • C. None of these
  • D. $$\angle BOC and \angle BAC$$ are supplementary

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 Single Correct Medium
In figure if $$BA\parallel DF, AD\parallel FG, \angle BAC=65^o$$ and $$\angle ACB=55^o$$, then find $$\angle FGH$$.
  • A. $$\angle FGH=145^o$$
  • B. $$\angle FGH=65^o$$
  • C. $$\angle FGH=55^o$$
  • D. $$\angle FGH=125^o$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 23rd 09, 2020

View Answer
Q5 Subjective Medium
List three other situations where reflex angles may be seen.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer