Question

in the figure , line a || line b and c is the transversal angle ABC = 3z° and angle BCD = 75° then value of z is.
a)25°
b)75°
c)50°
d)15°​

Answer 1

Answer:

The value of z is 25°.

Step-by-step explanation:

Given two straight lines a and b, where line a || line b

And c is the transversal line drawn across the parallel lines a and b.

The measure of angle ABC is 3z°.

And measure of angle BCD is 75°.

• When two parallel lines are crossed by a transversal, the pair of opposite angles of the transversal at the inner side of the parallel lines  are  called alternate interior angles.
• The measures of alternate interior angles are always equal.

So, in the present case, $\angle ABC ~\mbox{and} ~\angle BCD$ are the alternate interior angles, and hence they must be equal.

Therefore, $\angle ABC =\angle BCD$

$\implies3z =75\implies z =\dfrac{75}{3} =25^o$

Therefore, the value of z is 25°.

So, the correct answer is option 1.

For more info:

https://brainly.in/question/21114164

https://brainly.in/textbook-solutions/q-parallel-lines-intersected-transversal-pair-corresponding-angles-1