Mathematics

In the given figure, line l || line m and line n || p . Find $$\angle a,\angle b,\angle c.$$ from the given measure of an angle . 


SOLUTION
Let us mark the points R and S on line n, T and U on line p, A and B on line l and C and D on line m.
Suppose the lines n and p intersect the line l at K and L respectively and line m at M and N respectively.
Since, the line l and line p intersect at L, then 
$$\angle KLN = \angle BLT$$ (Vertically opposite angles)
$$\Rightarrow \angle KLN = 45^\circ$$
Since, line l $$\parallel$$ line m and line p is a transversal intersecting them at L and N, then
$$\angle KLN + \angle MNL = 180^\circ$$ (Pair of interior angles on the same side of transversal is supplementary)
$$\Rightarrow 45^\circ + \angle a = 180^\circ$$
$$\Rightarrow \angle a = 180^\circ - 45^\circ = 135^\circ$$
Since, the line m and line p intersect at N, then
$$\angle DNU = \angle MNL$$ (Vertically opposite angles)
$$\Rightarrow \angle b = \angle a = 135^\circ$$
Since, line n $$\parallel$$ line p and line m is a transversal intersecting them at M and N, then
$$\angle NMS = \angle DNU$$ (Corresponding angles)
$$\Rightarrow \angle c = \angle b = 45^\circ$$
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!


Subjective Medium Published on 09th 09, 2020
Next Question
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Find the angle whose complement is one third of its supplement.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q2 Subjective Medium
In the adjoining figure, if the angles $$\angle AOB, \angle BOC, \angle COD$$ are in the ratio $$1:2:3$$ and $$\overset{\leftrightarrow}{AD}$$ is a straight line, find the measures of all the angles.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q3 Single Correct Medium
Find the pair of parallel lines
  • A. AR;BX;Ap;BY
  • B. AQ;BZ;AP;BX
  • C. AQ;BX;AR;BZ
  • D. AQ;BY;AP;BZ

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 Assertion & Reason Medium
ASSERTION

If two lines intersect, then the vertically opposite angles are equal.

REASON

If a transversal intersects, two other parallel lines, then the sum of two interior angles on the same side of the transversal is $$180^o$$.

  • A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • B. Assertion is correct but Reason is incorrect
  • C. Both Assertion and Reason are incorrect
  • D. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q5 Subjective Medium
In Fig. write all the pairs of supplementary angles.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer