4. Find the value of x, y, z in each of the followings
please solve these questions
Answers
Answer:
i. x = 105° , y= 175° , z= 175°
ii. x= 30° , y= 110° , z =30°
iii. x= 110° , y= 110° , z= 110°
Formulas & theorems of a parallelogram.
- Opposite angles are equal like in fig. (i.)
y= z because they are opposite angles of a llgm.
- Adjacent angles of a llgm sum upto 180°
like in fig. (i.) x+z = 180° , x+ y = 180° , y+105° = 180°
IN QUESTION OR FIG. (ii.)
Because it is a llgm. Therefore it's opposite sides are equal and parallel.
So, if there are two parallel lines both intersected by a third line which is known as transversal then all the pairs of alternate interior angles are equal.
That's why in fig. ( ii.) x= z
In fig. ( iii.)
Linear pair axiom is used.
If you don't know what's linear pair axiom then see this —
If a ray stands on a line then the sum of the adjacent angles is equal to 180°
In all questions the following theorems, axioms & formulas are used. Same techniques have been followed in every question. I have not written the same again & again. I have given you an explanation on how to solve these kinds of questions.