Question

Find the value of x, y, and z when l || BC .

• A. x = 75°, y = 45° and z = 60°.
• B. x = 60°, y = 45° and z = 75°.
• C. x = 60°, y = 75° and z = 45°.
• D. x = 45°, y = 75° and z = 60°.

Answer 1

The correct option is C x = 60°, y = 75° and z = 45°.


Given, l || BC.

Considering AC as a transversal, z = 45°( Alternate interior angles) ...(i)

When AB is a transversal, y = 75° (Alternate interior angles) ...(ii)

Now, by angle sum property of triangle, x + y + z = 180°
From, (i) and (ii),
x + 75° + 45° = 180°
$\Rightarrow$ x + 120° = 180°
$\Rightarrow$ x = 180° - 120° = 60°.

Hence, x = 60°, y = 75° and z = 45°.