Question

find the measures of X y z in the figure, where L//BC

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Answer 1

Y=75
Z=45
X=180-(75+45)
=60

Answer 2

• Measure of x° is 60°.
• Measure of y° is 75°.
• Measure of z° is 45°.

Step-by-step explanation:

To find:-

• Measure of angles x°, y° and z°.

Construction:-

• Extend the line BC to the point P. So, PC is a line. And PC will parallel to line l .

Solution:-

We know,

Sum of two adjacent interior angles, when two lines are intersect by an transversal is 180°. This statement is known as Co-interior angles.

So,

➝ ∠1 + 75° = 180°

➝ ∠1 = 180° - 75°

➝ ∠1 = 105°

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

➝ 75° + x° + 45° = 180°

➝ x° + 120° = 180°

➝ x° = 180° - 120°

➝ x° = 60°

Similarly,

➝ ∠1 + y° = 180°

➝ 105° + y° = 180°

➝ y° = 180° - 105°

➝ y° = 75°

Sum of all interior angles of triangle is 180°.

➝ x° + y° + z° = 180°

➝ 60° + 75° + z° = 180°

➝ 135° + z° = 180°

➝ z° = 180° - 135°

➝ z° = 45°.