Question

if angle abc , AB = AC and Angle A is 40 degree find X and Y .

not goögle copied​

Answer 1

Answer:

$\Huge{\mathscr{\fcolorbox {blue}{pink}{\color {purple}{Answer}}}}$

In ∆ABC,

If,$\: \: \: \: \: \: \: \:$ AB = AC

then, $\: \: \: \: \: \: \:$∠ABC = ∠ACB

So,$\: \: \: \: \: \: \: \:$ Let ∠ABC be x.

then, $\: \: \: \: \: \: \: \:$∠ABC = ∠ACB = x

40° + x° + x° = 180° [∵ angle sum property of a triangle]

40° + 2x° = 180°

2x° = 180° - 40°

2x° = 140°

x° = $(\frac{140}{2})°$

x° = 70°

then, $\: \: \: \: \: \: \: \:$∠ABC = ∠ACB = 70°

180° - 70° = 110°

∴ $\df\green{\underline{\boxed{x°\: = \:y°\: =\: 110°}}}$

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Answer 2

Answer:

$\fbox\red{since ∆ABC is isosceles with}$

$\small\pink{AB\: =\: AC}$

$\small\pink{∆ACB\: =\: ∆ABC}$

$\huge\blue{now}$

• $\tt\green{∆A\: + \: ∆ABC\:+\:∆ ACB}$ = 180°
• 40° + ∆ABC + ∆ACB = 180°
• 2∆ABC = 180° - 40°
• 2∆ABC = 140°
• ∆ABC = 140/2 = 70°

$\huge\blue{now}$

• ∆ABC + x° = 180°
• 70° + x° = 180°
• x° = 180° - 70°
• x° = 110°

$\huge\blue{again}$

• ∆ABC + y° = 180°
• 70 + y° = 180°
• y° = 180° - 70°
• y° = 110°

hence. x = 110 , y = 110