
In the figure, AB II CD, find x.
Answer
561.9k+ views
Hint: Draw a line parallel to AB and CD and use the concept and relations between angles when two parallel lines intersected by a transversal. By drawing parallel line angle x is divided into two parts, find each part and then add to get the value of x.
Complete step-by-step answer:
Put a point E associated with angle x as in figure. Draw a line FE parallel to AB and CD and pass through E.
Now, extend BE and CE as shown in figure.
AB and FE are parallel and BE is transversal.
Therefore, ∠ ABE + ∠ FEB = 180°
[If two lines are parallel and a transversal intersecting the two lines, then sum of interior angles on the same side of transversal is equal to 180°]
Given that ∠ ABE = 48°
⇒ 48° + ∠ FEB = 180° ⇒ ∠ FEB = 180° − 48° = 132°
Also, DC and FE are parallel and CE is transversal.
Therefore, ∠ DCE + ∠ FEC = 180°
[If two lines are parallel and a transversal intersecting the two lines, then sum of interior angles on the same side of transversal is equal to 180°]
Given that ∠ DCE = 24°
⇒ 24° + ∠ FEC = 180° ⇒ ∠ FEC = 180° − 24° = 156°
Now, ∠x = ∠ FEB + ∠ FEC = 132° + 156° = 288°
Therefore, ∠ x = 288°
Note: In these types of questions, draw the lines parallel of perpendicular whichever required to apply the theorem or concepts. You must know the parallel lines and it’s transversal to establish the relations between angles. You must use terms like alternate interior angle, corresponding angles, opposite angles etc.
Complete step-by-step answer:
Put a point E associated with angle x as in figure. Draw a line FE parallel to AB and CD and pass through E.
Now, extend BE and CE as shown in figure.
AB and FE are parallel and BE is transversal.
Therefore, ∠ ABE + ∠ FEB = 180°
[If two lines are parallel and a transversal intersecting the two lines, then sum of interior angles on the same side of transversal is equal to 180°]
Given that ∠ ABE = 48°
⇒ 48° + ∠ FEB = 180° ⇒ ∠ FEB = 180° − 48° = 132°
Also, DC and FE are parallel and CE is transversal.
Therefore, ∠ DCE + ∠ FEC = 180°
[If two lines are parallel and a transversal intersecting the two lines, then sum of interior angles on the same side of transversal is equal to 180°]
Given that ∠ DCE = 24°
⇒ 24° + ∠ FEC = 180° ⇒ ∠ FEC = 180° − 24° = 156°
Now, ∠x = ∠ FEB + ∠ FEC = 132° + 156° = 288°
Therefore, ∠ x = 288°
Note: In these types of questions, draw the lines parallel of perpendicular whichever required to apply the theorem or concepts. You must know the parallel lines and it’s transversal to establish the relations between angles. You must use terms like alternate interior angle, corresponding angles, opposite angles etc.
Recently Updated Pages
Master Class 8 Social Science: Engaging Questions & Answers for Success

Master Class 8 Science: Engaging Questions & Answers for Success

Master Class 8 Maths: Engaging Questions & Answers for Success

Class 8 Question and Answer - Your Ultimate Solutions Guide

Full form of MODEM?

What is a numerical label assigned to each device in a network?

Trending doubts
What is BLO What is the full form of BLO class 8 social science CBSE

What is 1 divided by 0 class 8 maths CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Citizens of India can vote at the age of A 18 years class 8 social science CBSE

Today is Monday After 61 days it will be aWednesda-class-8-maths-CBSE

Write a letter to your class teacher asking for 2 days class 8 english CBSE

