Question

i need the ANSWER to this question pls I can't find it on brainly ​

Answer 1

Solution :-

a)

From the given figure,

x+55° and (3x-65)° are alternative interior angles.

We know that

If two parallel lines are intersected by a transversal then the pair of alternative interior angles are equal.

Therefore, x+55° = 3x-65°

=> 55°+65° = 3x-x

=> 120° = 2x

=> 2x = 120°

=> x = 120°/2

=> x = 60°

The value of x = 60°

b)

We have, x = 60°

x+55° = 60°+55° = 115°

3x-65° = 3(60°)-65° = 180°-65° = 115°

From the given figure ,

x+55° and a are vertically opposite angles which are equal.

Therefore, a = 115°

We know that

a and c are linear pair

=> a+c = 180°

=> 115° +c = 180°

=> c = 180°-115°

=> c = 65°

b and c are vertically opposite angles

=> b = c

=> b = 65°

b and d are corresponding angles which are equal

b = d

=> d = 65°

c and f are corresponding angles which are equal

=> c = f

=> f = 65°

b and e are the exterior angles on the same side to the transversal which are Supplementary.

=>b+e = 180°

=> 65° + e = 180°

=> e = 180°-65°

=> e = 115°

Answer :-

• The value of x = 60°

• a = 115°

• b = 65°

• c = 65°

• d = 65°

• e = 115°

• f = 65°

Used formulae:-

If two parallel lines are intersected by a transversal then,

→ Corresponding angles are equal.

→ Alternative interior angles are equal.

→ Interior angles on the same side to the transversal are Supplementary.

→ Exterior angles on the same side to the transversal are Supplementary.

→ Vertically opposite angles are equal.

Answer 2

Step-by-step explanation:

Solution :-

a)

From the given figure,

x+55° and (3x-65)° are alternative interior angles.

We know that

If two parallel lines are intersected by a transversal then the pair of alternative interior angles are equal.

Therefore, x+55° = 3x-65°

=> 55°+65° = 3x-x

=> 120° = 2x

=> 2x = 120°

=> x = 120°/2

=> x = 60°

The value of x = 60°

b)

We have, x = 60°

x+55° = 60°+55° = 115°

3x-65° = 3(60°)-65° = 180°-65° = 115°

From the given figure ,

x+55° and a are vertically opposite angles which are equal.

Therefore, a = 115°

We know that

a and c are linear pair

=> a+c = 180°

=> 115° +c = 180°

=> c = 180°-115°

=> c = 65°

b and c are vertically opposite angles

=> b = c

=> b = 65°

b and d are corresponding angles which are equal

b = d

=> d = 65°

c and f are corresponding angles which are equal

=> c = f

=> f = 65°

b and e are the exterior angles on the same side to the transversal which are Supplementary.

=>b+e = 180°

=> 65° + e = 180°

=> e = 180°-65°

=> e = 115°

Answer :-

• The value of x = 60°

• a = 115°

• b = 65°

• c = 65°

• d = 65°

• e = 115°

• f = 65°

$answer}$