Question

If angle A is 50° , angle B is x°, angle C is unknown and the exterior angle as in the angle D is 115°, find the value of x​. I need step by step​

Answer 1

Answer :-

• ∠B = 65° or x = 65°$.$

Given :-

• Angle A is 50°
• Angle B is x°
• Angle C is unknown.
• The exterior angle as in the angle D is 115°.

To find :-

• Find the value of x.

Solution :-

∠ADB + 115° = 180°

∠ADB = 180° - 115°

∠ADB = 65°

We know that,

Sum of interior angles of a ∆ = 180°

65° + 50° + x° = 180°

115° + x° = 180°

x° = 180° - 115°

x° = 65°

Hence, ∠B = 65° or x = 65°.

Therefore, Angles of the triangle are :-

1. Angle A = 50°
2. Angle B = 65°
3. Angle C = 65°
4. Angle D = 115°

Answer 2

AnswEr-:

$\boxed {\mathrm{ \angle B \:or\: x \: = 65^{⁰} }}$

Explanation-:

$\sf{ Given-:}$

• Angle A = 50⁰,

• Angle B = x⁰,

• Angle C is unknown and

• The exterior angle as in the angle D = 115°

$\sf{ To\:Find-:}$

• The value of x⁰ .

$\dag{\underline {\mathrm{Solution\:of\:Question\:-:}}}$

As we know that ,

• $\longrightarrow {\sf{\angle ADB + \angle ACB = 180^{⁰}}}$

• $\sf{ Here-:}$

• $\sf{ \angle ADB = 115^{⁰}}$

• $\sf{ \angle ACB = ??}$

Now , By putting known Values-:

• $\longrightarrow {\sf{\angle ADB + \angle ACB = 180^{⁰}}}$

• $\longrightarrow {\sf{\angle ACB = 180^{⁰}}}$

• $\longrightarrow {\sf{\angle ACB = 180-115}}$

• $\longrightarrow {\sf{\angle ACB = 65^{⁰}}}$

Therefore,

• $\longrightarrow {\sf{\angle ACB \:or \: \angle C \: = 65^{⁰}}}$________[1]

Now ,

As , We know That -:

• $\dag{\underline {\mathrm{Total \:Sum\:of\:interior \:angle \:of\:Triangle\:is\:180^{⁰}}}}$

Or ,

• $\dag{\underline {\mathrm{\angle A + \angle B + \angle C = 180^{⁰}}}}$

Here -:

• Angle A = 50⁰ ( Given that )

• Angle B = x⁰

• Angle C = 65⁰ ( From 1)

Now , By putting known Values in Formula of sum of angle of triangle-:

• $\longrightarrow {\mathrm{50^{⁰} + 65^{⁰} + x = 180^{⁰}}}$

• $\longrightarrow {\mathrm{ 115^{⁰} + x = 180^{⁰}}}$

• $\longrightarrow {\mathrm{ x = 180 - 115 }}$

• $\longrightarrow {\mathrm{ x = 65^{⁰} }}$

Then ,

• Putting x = 65⁰

• Angle B = x = 65⁰

Hence ,

• $\boxed {\mathrm{ \angle B \:or\: x \: = 65^{⁰} }}$

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