Question

In ABC side BC is produced to D. If angle ABC=50° and angle ACD=110° then angle A ?​

Answer 1

Answer:

60°

Step-by-step explanation:

Consider ∆ABC

Given that angle ABC=50°

Angle ACD=110°

So now angle BCA=x

So x+angleC=180°(angle c is considered from angle ACD,so see in diagram that angle on a stringht line =180°)

x+110°=180°

x=180°-110°

x=70°

therefore angle BCA=70°

Now consider ∆ABC

In triangle ABC

Angle A=?

Angle B=50°

Angle C=70°

Now you keep angle A as x

x+Angle B+Angle C=180°(Sum of angles in a triangle)

x+50+70=180

x=180-120

x=60°

Angle A =60°

Answer 2

Answer:

60°

Step-by-step explanation:

Concept= Sum of Angles

Given= Two angles

To find= An unknown angle

Explanation=

We have been given the question as in ABC side BC is produced to D. If angle ABC=50° and angle ACD=110° then angle A ?​

So ΔABC has three angles

∠ABC,∠BCA and ∠BAC

If BC is produced to D then the angle made by them is ∠ACD.

Now this  ∠BCA and ∠ACD lie on the same line. Their sum will be equal to 180° as the sum of angles on straight line is 180°.

We are known with the values of ∠ABC=50°

∠ACD=110°

So now,

∠ACD + ∠BCA =180°

110° + ∠BCA= 180°

∠BCA = 180-110= 70°

Therefore we get to know that  ∠BCA=70°

So now in ΔABC,

we know following angles

∠BCA=70°, ∠ABC=50°

Sum of angles of triangles is 180°. This is a property of triangle.

∠BCA + ∠ABC + ∠BAC= 180°

70° + 50° +∠BAC = 180°

∠BAC= 180-120= 60°

Therefore the angle A will be 60°.

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