Question

in trianglr ABC,ray AC is extended to point D.if angle A=50° and angle B=30°.find angle ACD​

Answer 1

Answer:

Angle C= 100°

Step-by-step explanation:

Because Measurement of an triangle is 180°

Answer 2

Step-by-step explanation:

Given,

• ∠A = 50°
• ∠B = 30°

To find,

• ∠C

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(5,1)\qbezier(5,1)(5,1)(3,4)\qbezier(3,4)(3,4)(1,1)\qbezier(5,1)(5,1)(8,1)\put(0.5,0.5){\sf B}\put(3,4.5){\sf A}\put(5,0.5){\sf C}\put(8,0.5){\sf D}\qbezier(1.4,1)(1.4,1.1)(1.2,1.3)\put(1.7,1.3){ \sf 30^{\circ} }\qbezier(2.8,3.6)\qbezier(3,3.5)\qbezier(3.2,3.6)\put(2.7,3){ \sf 50^{\circ} }\end{picture}$

How to find?

Here, we can find easily ∠C with the Angle sum property of ∆. But here in the question, there is also it mentions "AC is extended to point D" which means the questioner wants us to find it by another long method.

Here, we shall find ∠D and then find ∠C.

Required Knowledge :

• The exterior of a ∆ is equal to the sum of the 2 interior opposite angles.
• Supplementary angles = 180°

We shall find the solution by the 2nd method to satisfy the questioner.

Finding ∠D :

∠A + ∠B = ∠D

⇒50° + 30° = ∠D

⇒80° = ∠D

.°. ∠D = 80°

Finding ∠C :

∠C + ∠D = 180°

⇒∠C + 80° = 180°

⇒∠C = 180° - 80°

⇒∠C = 100°

.°. ∠C = 100°

Hence, ACD = 100°.

Let's Check It :

∠A + ∠B + ∠C = 180° [ °.° Angle sum of a ∆]

⇒50° + 30° + 100° = 180°

⇒80° + 100° = 180°

⇒180° = 180°

Hence, ACD = 100° is the correct solution.