Question

please answer the question​

Answer 1

Answer :

• a) 43.5°
• b) 30°
• c) 57°

Solution :

Given angles :

• Angles of ∆ABC are x° , 2x° , (x+6)°.
• Angles of ∆LMN are 3x° , 2x°, x°.
• Angles of ∆DEF are (x+3)°, (x+4)°, (x+2)°.

To Find :

• Value of x.

$\red\bigstar\: \boxed{\sf Sum \: of \: angles \: all \: angles \: of \: triangle = 180\degree }$

Using this concept , we can find the value of x. So, we will add all the angles and put equal to 180° . As we know sum of all angles of triangle will equal to 180° . Then, By simplifying we will get the value of x.

Let's do,

a) For triangle ABC.

➩ x + 2x° + (x+6)° = 180°

➩ x + 2x° + x+6° = 180°

➩ 4x + 6° = 180°

➩ 4x = 174°

$\leadsto \underline{\boxed{\pink{\sf x = 43.5°}}}$

━━━━━━━━━━━━━━

b) For ∆LMN.

➩ 3x° + 2x°+ x° = 180°

➩ 6x = 180°

$\leadsto \underline{\boxed{\pink{\sf x = 30°}}}$

━━━━━━━━━━━━━━

c) For ∆DEF.

➩ (x+3)°+ (x+4)°+ (x+2)° = 180°

➩ x+3°+ x+4°+ x+2° = 180°

➩ 3x + 9 = 180°

➩ 3x = 171°

$\leadsto \underline{\boxed{\pink{\sf x = 57°}}}$

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