Question

In the given figure, if AB||CI || EF and angle x: angle y=2:3 find the value of angle Z​

Answer 1

Given : AB || CD || EF and ∠x : ∠y = 2 : 3

To find : Value of ∠z

Solution :

We are given that the ratio of ∠x and ∠y is 2 : 3.

We are aware about the co-interior angle property of straight lines. Sum of two co-interior angle is always equal to 180°.

Let's assume the ratio of ∠x : ∠y be 2a : 3a.

Now,

=> 2a + 3a = 180° ( By co interior angle )

=> 5a = 180°

=> a = 180°/5

=> a = 36°

Therefore,

• ∠x = 2a = 2 × 36° = 72°
• ∠y = 3a = 3 × 36° = 108°

We are also aware about the alternate interior angle property of parallel straight lines. Alternate interior angles are always equal to each other.

Now, consider parallel lines AB and EF, and PQ be the transversal :

=> ∠x = ∠z ( By alternate interior angle )

Hence ∠z = 72°

Answer 2

Answer:

72

Step-by-step explanation:

2a+3a=180

a=36

2x36=72

according to congruent angles z=72