**Angles formed by parallel lines and transversals:**

A straight line that intersects two or more straight lines at distinct points is called as transversal.

More clearly,

A straight line intersecting two parallel lines.

From the above figure, we can get the angles formed by parallel lines and transversals.

Vertically opposite angles are equal. |
< 1 = < 3 < 2 = < 4 < 5 = < 7 < 6 = < 8 |

Corresponding angles are equal. |
< 1 = < 5 < 2 = < 6 < 3 = < 7 < 4 = < 8 |

Alternate interior angles are equal. |
< 3 = < 5 < 4 = < 6 |

Alternate exterior angles are equal. |
< 1 = < 7 < 2 = < 8 |

Consecutive interior angles are supplementary. |
< 3 + < 6 = 180° < 4 + < 5 = 180° |

**Problem 1 :**

In the figure given below, let the lines l₁ and l₂ be parallel and m is transversal. If <F = 65°, find the measure of each of the remaining angles.

**Solution : **

From the given figure,

< F and < H are vertically opposite angles and they are equal.

Then, < H = < F -------> < H = 65°

< H and < D are corresponding angles and they are equal.

Then, < D = < H -------> < D = 65°

< D and < B are vertically opposite angles and they are equal.

Then, < B = < D -------> < B = 65°

< F and < E are together form a straight angle.

Then, we have

< F + < E = 180°

Plug < F = 65°

< F + < E = 180°

65° + < E = 180°

< E = 115°

< E and < G are vertically opposite angles and they are equal.

Then, < G = < E -------> < G = 115°

< G and < C are corresponding angles and they are equal.

Then, < C = < G -------> < C = 115°

< C and < A are vertically opposite angles and they are equal.

Then, < A = < C -------> < A = 115°

**Therefore, **

**< A = < C = < E = < G = 115°**

**< B = < D = < F = < H = 65°**

**Problem 2 :**

In the figure given below, let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x"

**Solution : **

From the given figure,

< (2x + 20)° and < (3x - 10)° are corresponding angles.

So, they are equal.

Then, we have

2x + 20 = 3x - 10

30 = x

**Hence, x = 30°**

**Problem 3 :**

In the figure given below, let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x"

**Solution : **

From the given figure,

< (3x + 20)° and < 2x° are consecutive interior angles.

So, they are supplementary.

Then, we have

3x + 20 + 2x = 180°

5x + 20 = 180°

5x = 160°

x = 32°

**Hence, x = 32°**

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