Question

Choose the correct option for angles B and C 


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Answer 1

Answer:

Given :

• Angle A = 75°
• CE || AB
• Angle ECD = 40°

To find :

• Angle B and Angle C of triangle ABC

Solution :

It is given that, CE || AB, and we can see that AC is a transversal line on parallel lines CE and AB, so we conclude that,

Angle BAC = Angle ECA (Alternate interior angle)

75° = Angle ECA

• Now, we have to find Angle ACB of triangle ABC.

We know that, BCD is a straight line.

So, we can find Angle ACB by linear pair of angles.

Angle ACB + Angle ECA + Angle ECD = 180°

Angle ACB + 75° + 40° = 180°

Angle ACB + 115° = 180°

Angle ACB = 180° - 115°

Angle ACB = 65°

$\implies$ Hence, Angle C of triangle ABC is 65°.

• Now, we have to find Angle B of triangle ABC.

We know that, sum of angles of triangle is 180°.

So,

Angle B + Angle ACB + Angle A = 180°

Angle B + 65° + 75° = 180°

Angle B + 140° = 180°

Angle B = 180° - 140°

Angle B = 40°

$\implies$ Hence, Angle B of triangle ABC is 40°.

Answer 2

Answer:

Angle B = 40°

Step-by-step explanation:

Given :

• Angle A = 75°
• CE || AB
• Angle ECD = 40°

To find :

Angle B and Angle C of triangle ABC

Solution :

It is given that, CE || AB, and we can see that AC is a transversal line on parallel lines CE and AB, so we conclude that,

Angle BAC = Angle ECA (Alternate interior angle)

75° = Angle ECA

• Now, we have to find Angle ACB of triangle ABC.
• Now, we have to find Angle ACB of triangle ABC.We know that, BCD is a straight line.

So, we can find Angle ACB by linear pair of angles.

Angle ACB + Angle ECA + Angle ECD = 180°

Angle ACB + 75° + 40° = 180°

Angle ACB + 115° = 180°

Angle ACB = 180° - 115°

Angle ACB = 65°

⟹ Hence, Angle C of triangle ABC is 65°.

Now, we have to find Angle B of triangle ABC.

We know that, sum of angles of triangle is 180°.

So,

Angle B + Angle ACB + Angle A = 180°

Angle B + 65° + 75° = 180°

Angle B + 140° = 180°

Angle B = 180° - 140°

Angle B = 40°

⟹ Hence, Angle B of triangle ABC is 40°.

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