In the adjoining figure, line p // line l // line q. Find angle x with the measures given in the figure.
Answers
Answer:
answer is 70°
Step-by-step explanation:
given: p//l//q and <pso=40°, <qto= 30°
solution:-
p//l and SO is the transversal,
then, <pso=<mos = 40°(vertically opposite angle)
similarly l//q and OT is the transversal
then, ,<qto=<mot= 30° (vertically opposite angle)
but, <sot or <x= <som+<tom
=40°+30°
=70°
hope this help. please mark brainliest
Answer:
The measure of angle x is 70°.
Step-by-step-explanation:
NOTE: Kindly refer to the attachment for the diagram.
We have to mark some points on the lines given in the figure.
The points A, L and B on line p.
The points C and D on line l.
The points P and Q on line q.
Now, line AB || line CD and line LM is a transversal,
∴ m∠LMD = m∠ALM - - [ Alternate interior angles ]
∴ m∠LMD = 40°
Now, line CD || line PQ and line MN is a transversal,
∴ m∠DMN = m∠PNM - - [ Alternate interior angles ]
∴ m∠DMN = 30°
Now,
∴ m∠LMD + m∠DMN = 40° + 30°
∴ m∠LMN = 70°
∴ x = 70°
Additional Information:
1. Parallel lines:
The lines which do not meet each other when extended are called as parallel lines.
2. Intersecting lines:
The lines which meet each other in a point are called as intersecting lines.
3. Transversal:
A line which divides one or more lines in two distinct parts is called a transversal.
4. Properties related to Parallel lines and Transversals:
A. Corresponding Angles Property
B. Alternate Angles Property
C. Interior Angles Property
5. Corresponding Angles Property:
The corresponding angles formed by parallel lines and their transversals are of equal measures.
6. Alternate Angles Property:
The alternate angles formed by parallel lines and their transversals are of equal measures.
7. Interior Angles Property:
The interior angles formed by parallel lines and their transversals are supplementary angles i. e. their sum is 180°.
