Question

In the adjoining figure, line a line b. line 1 is a transversal. Find the measures of Z x, Zy, Z z using the given information.​

Answer 1

Answer:

Let us mark the points A and B on l; K and M on a; L and N on b.

Suppose KM and LN intersect AB at P and Q respectively.

Since, a||b and l is a transversal, then

m∠PQL = m∠APK (Corresponding angles)

⇒ x = 105°

Since, AB and LN are straight lines that intersect at Q, then

m∠BQN = m∠PQL (Vertically opposite angles)

⇒ y = x

⇒ y = 105°

Since, AB is a straight line and ray QN stands on it, then

m∠BQN + m∠PQN = 180° (Angles in linear pair)

⇒ y + m∠PQN = 180°

⇒ 105° + m∠PQN = 180°

⇒ m∠PQN = 180° − 105°

⇒ m∠PQN = 75°

Now, m∠APM = m∠PQN (Corresponding angles)

⇒ z = 75°

Step-by-step explanation:

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Answer 2

Answer:

i. line a || line b and line l is a transversal. ∴ m∠x = 105° …

i. line a || line b and line l is a transversal. ∴ m∠x = 105° …(i) [Corresponding angles]

i. line a || line b and line l is a transversal. ∴ m∠x = 105° …(i) [Corresponding angles] ii. m∠y = m∠x … [Vertically opposite angles] ∴ m∠y = 105° …[From (i)]

i. line a || line b and line l is a transversal. ∴ m∠x = 105° …(i) [Corresponding angles] ii. m∠y = m∠x … [Vertically opposite angles] ∴ m∠y = 105° …[From (i)] iii. m∠z + 105° = 180° …[Angles in a linear pair]

i. line a || line b and line l is a transversal. ∴ m∠x = 105° …(i) [Corresponding angles] ii. m∠y = m∠x … [Vertically opposite angles] ∴ m∠y = 105° …[From (i)] iii. m∠z + 105° = 180° …[Angles in a linear pair] ∴ m∠z = 180°- 105°

i. line a || line b and line l is a transversal. ∴ m∠x = 105° …(i) [Corresponding angles] ii. m∠y = m∠x … [Vertically opposite angles] ∴ m∠y = 105° …[From (i)] iii. m∠z + 105° = 180° …[Angles in a linear pair] ∴ m∠z = 180°- 105° ∴ m∠z = 75°

i. line a || line b and line l is a transversal. ∴ m∠x = 105° …(i) [Corresponding angles] ii. m∠y = m∠x … [Vertically opposite angles] ∴ m∠y = 105° …[From (i)] iii. m∠z + 105° = 180° …[Angles in a linear pair] ∴ m∠z = 180°- 105° ∴ m∠z = 75° ∴ m∠x = 105°, m∠y = 105°, m∠z=75°

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