In the given figure, l || m and p || q. Find the angles x, y, z and t.

The angles at the top intersection point (where lines l, q and the vertical line meet) must sum to 360° because they form a complete circle.

270° + 40° + x° = 360°

⇒ 310° + x° = 360°

⇒ x° = 360° - 310°

⇒ x° = 50°

Consider p || q:

z° = x° $\quad$[Corresponding angles]

∴ z° = 50°

Similarly,

y° = 40° $\quad$[Corresponding angles]

Since, p is a straight line:

z° + t° = 180° $\quad$[Linear pair]

⇒ 50° + t° = 180° $\quad$[Substituting the value of z]

⇒ t° = 180° - 50°

⇒ t° = 130°

x° = 50°, y° = 40°, z° = 50° and t° = 130°