Question

ABC is an isosceles triangle in which AB = AC . find the value of x in each case​

Answer 1

Answer:

x=45°

Step-by-step explanation:

Here, <A = 90° (Right angle)

Here, AB = AC (Given)

So, <B = <C = x

We know that sum of interior angles of a triangle is 180°.

So, <A+<B+<C = 180°

=> 90°+x+x = 180°

=> 2x = 90°

=> x = 45°

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Answer 2

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${ \bold { \underline{\large{Correct \: Question : - }}}} \:$

ABC is an isosceles triangle in which AB = AC and ∠BAC = 90° find the value of x in each case.

${ \bold { \underline{\large{Given : - }}}} \:$

◍ $\sf{\triangle{ABC}\: in\: which\: AB \:= \:AC}$

◍$\sf{\angle{BAC}\: = \:90\degree}$

${ \bold { \underline{\large{To \: Find : - }}}} \:$

◍ $\sf{Value\:of\:x}$

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$\large\boxed{\boxed{\tt{So\:let's \:do\:it\::-}}}$

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${ \bold { \underline{\large{Solution : - }}}} \:$

Let ∠ABC = y and ∠BAC = z !

Angle opposite to equal sides are equal.

∴ x = y

Now,

$\sf{\red \dag \underbrace{Sum\:of\:all\:angles\:of\:triangle\:=\:180\degree}}\red\dag$

ㅤㅤㅤㅤ$\sf{x\:+\:y\:+\:z\:=\:180\degree}$

We know, x = y . So, we can add them.

ㅤㅤㅤㅤ$\sf{2x\:+\:90\degree\:=\:180\degree}$

ㅤㅤㅤㅤ$\sf{2x\:=\:180\degree\:-\:90\degree}$

ㅤㅤㅤㅤ$\sf{2x\:=\:90\degree}$

ㅤㅤㅤㅤ$\sf{x\:=\:\dfrac{90\degree}{2}}$

ㅤㅤㅤㅤ$\sf{x\:=\:45\degree}$

$\boxed {\frak {\therefore \purple {\angle{ACB}\:=\:\angle{ABC}\:=\:45\degree}}}\:\orange\bigstar$

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$\sf{\red \dag \underbrace{Verification}}\red\dag$

$\sf{\angle{ABC}\:+\:\angle{ACB}\:+\:\angle{BAC}\:=\:180\degree}$

$\sf{45\degree\:+\:45\degree\:+\:90\degree\:=\:180\degree}$

$\sf{90\degree\:+\:90\degree\:=\:180\degree}$

$\sf{180\degree\:=\:180\degree}$

$\boxed {\frak \purple {Hence\:verified}}\:\orange\bigstar$

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${ \bold { \underline{\large \red {Note : - }}}} \:$

$\sf{Diagram\: is\: in\: the \:attachment!}$

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