Question

In the following figure, the side BC of
triangle ABC is extended up to the point D.
If angle is equal to 55° and <B = 60°, then
the measure of <ACB is​

Answer 1

Given:-

• Measure of ∠B is 60°.
• Measure of ∠A is 55°.

To find:-

• Measure of ∠ACB.

Solution:-

By First method.

We know that,

Sum of all interior angles of triangle is 180°.

So,

⇒ ∠ACB + ∠A + ∠B = 180°

⇒ ∠ACB + 55° + 60° = 180°

⇒ ∠ACB + 115° = 180°

⇒ ∠ACB = 180° - 115°

⇒ ∠ACB = 65°

Therefore,

∠ACB is 65°

By second method:-

We know that,

Sum of any two interior angles of triangle equal to opposite exterior exterior.

⇒ ∠ACD = ∠A + ∠B

⇒ ∠ACD = 55° + 60°

⇒ ∠ACD = 115°.

And we also know that,

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

So,

⇒ ∠ACD + ∠ACB = 180° [Linear pair]

⇒ 115° + ∠ACB = 180°

⇒ ∠ACB = 180° - 115°

⇒ ∠ACB = 65°

Therefore,

∠ACB is 65°.

______________________

∠ACB is 65°

∠ACD is 115°

Answer 2

Answer:

Step-by-step explanations :

<A = 55°

<B = 60°

So , we should add

55° + 60° =115°