Question

in the given figure segment shown by arrow heads are parallel .find the value of x and y ​

Answer 1

Answer:

x = 30, y = 75

Step-by-step explanation:

Angle x = 30 degrees

The reason is angle x and angle 30 are alternate interior angles on the transversal line and alternate interior angles are equal.

Now,

angle x + angle 45 = angle y (Exterior angle of triangle is equal to sum of opposite interior angles.)

Therefore,

30 + 45 = angle y

angle y = 75 degrees

Thus,

x = 30, y = 75

Answer 2

• Measure of x° is 30°.
• Measure of y° is 75°

Step-by-step explanation:

To find:-

• Measure of x and y.

Solution:-

☘ By First method:-

In given figure,

Two lines are parallel.

We know,

Alternative interior angles are equal, When two parallel lines are intersect by an transversal.

So, x° = 30°

Sum of all angles of triangle is equal to 180°

➝ x° + 45° + ∠1 = 180°

➝ 30° + 45° + ∠1 = 180°

➝ 75° + ∠1 = 180°

➝ ∠1 = 180° - 75°

➝ ∠1 = 105°

We also know,

Sum of all angles forms on straight line is equal to 180°. This statement is known as linear pair.

So,

➝ ∠1 + y° = 180°

➝ 105° + y° = 180°

➝ y° = 180° - 105°

➝ y° = 75°

☘ By second method :-

x° = 30° [By alternative interior angles]

We know that,

Sum of any two interior angles of triangle is equal to one opposite exterior angle of triangle.

So,

➝ y° = x° + 45°

➝ y° = 30° + 45°

➝ y° = 75°