Question

line l and line m are parallel and line n is the transversal, angle a= 85 degree, find angle b and angle c​

Answer 1

• Angle b is 85°.
• Angle c is 85°.

Step-by-step explanation:

To find:-

• Measure of angle b and Angle c.

Solution:-

If two lines are bisect or intersect, then there vertical opposite angles are equal.

Here, l is a line which is intersecting by n.

So, ∠b = ∠a = 85° [Given, ∠a = 85°]

We also know,

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

So,

➝ ∠1 + ∠b = 180°

➝ ∠1 + 85° = 180°

➝ ∠1 = 180° - 85°

➝ ∠1 = 95°

We also know,

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

So,

➝ ∠c + ∠1 = 180°

➝ ∠c + 95° = 180°

➝ ∠c = 180° - 95°

➝ ∠c = 85°

Therefore,

Angle b is 85°.

Angle c is 85°.

Answer 2

Angle b is 85°.

Angle c is 85°.

Step-by-step explanation:

To find:-

Measure of angle b and Angle c.

Solution:-

If two lines are bisect or intersect, then there vertical opposite angles are equal.

Here, l is a line which is intersecting by n.

So, ∠b = ∠a = 85° [Given, ∠a = 85°]

We also know,

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

So,

➝ ∠1 + ∠b = 180°

➝ ∠1 + 85° = 180°

➝ ∠1 = 180° - 85°

➝ ∠1 = 95°

We also know,

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

So,

➝ ∠c + ∠1 = 180°

➝ ∠c + 95° = 180°

➝ ∠c = 180° - 95°

➝ ∠c = 85°

Therefore,

Angle b is 85°.

Angle c is 85°.