Question

$\sf{ \orange{ \underline{Heya \: Folks!!}}}$
$\large \underbrace{ \sf{ \color{magenta}{Question\;:}}}$
In the isosceles triangle ABC, ∠A and ∠B are equal. ∠ACD is an exterior angle of ∆ABC. The measures of ∠ACB and ∠ACD are (3x-17) and (8x+10)° respectively.
Find the measures of ∠CB and ∠CD.
Also find the measures of ∠A and ∠B.
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Answer of the question - m∠ACB = 34° , m∠ACD = 146°, m∠A = m∠B = 73°.

Class 7th maths question! (CBSE syllabus)
Chapter name - Angles and pairs of angles.
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Note : Step by step Explanation & Diagram required! And also some fun math problems. It would be okay if you don't skip any single step! :D
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Answer 1

$\huge{\underline{\underline{\sf{\purple{Given:-}}}}}$

∆ABC is an isosceles triangle where <A=<B.

<ACD is an exterior angle of ∆ABC .

<ACB = (3x-17)°

<ACD = (8x+10)°

$\huge{\underline{\underline{\sf{\purple{To\:find:-}}}}}$

We have to find out the angles <A, <B, <ACB, <ACD.

$\huge{\underline{\underline{\sf{\purple{Figure:-}}}}}$

Refer the attachment.

$\huge{\underline{\underline{\sf{\purple{Solution:-}}}}}$

<ACB + <ACD = 180° (Linear pair)

(3x-17)° + (8x+10)° = 180°

3x-17+8x+10 = 180°

11x-7 = 180°

11x = 180° + 7

x = 187/11

x = 17

==> <ACD = (8x+10)° = 146°

==> <ACB = (3x-17)° = 34°

<A=<B (Given)

Let the unknown angle be z.

z + z + <ACB = 180° (Angle sum property)

2z + 34° = 180°

2z = 180° - 34°

z = 146°/2

z = 73°

==> <A = <B = 73°

☺️శుభోదయం☺️

Answer 2

Given:

In the isosceles triαngle ABC,

➨ m∠A = m∠B

➨ ∠ACD is an exterior αngle of ∆ABC

➨ m∠ACB = (3x - 16)°

➨ m∠ACD = (8x + 10)°

➨ m∠ACD + m∠ACB = 180° ––——- αngles in α lineαr pαir.

➨ (8x + 10) + (3x - 17) = 180

➨ 8x + 10 + 3x - 17 = 180

➨ 11x - 7 = 180

⠀⠀∴ 11x = 180 + 7

⠀⠀∴ 11x = 187

⠀⠀∴ x = $\large\sf{\cancel\frac{187}{11}}$

$\boxed{ \sf{ \orange{x \: = 17}}}$

➨ m∠ACB = 3x - 17 = 3 × 17 = 51 - 17

⠀⠀∴ m∠ACB = 34°

$\boxed{ \sf{ \orange{m \angle ACD = 146°}}}$

By property,

the meαsure of αn exterior αngle of α triαngle is equαl to the sum of the meαsures of its remote interior αngles.

∴ m∠A = 73°

∴ m∠B = 73°

Answer:

m∠ACB = 34°

m∠ACD = 146°

m∠A = m∠B = 73°.