Question

in the figure fin the valud of x​

Answer 1

$\large \underline{ \underline{ \text{Question:}}}$

• In the Attachment.

$\large \underline{ \underline{ \text{Solution:}}}$

Given that,

• $\angle ABC = 2x + {40}^{ \circ}$
• $\angle BCA = 3x - {80}^{ \circ}$

And,

• $\angle BAC = 5x - {60}^{ \circ}$

According to Universal laws of triangle. The sum of all angles of a triangle should be 180°. So we can say that, The sum of all angles of ∆ABC is equals to 180°.

Can be written as,

• $\angle ABC + \angle BCA + \angle BAC = {180}^{ \circ}$

Substituting the given values,

$\implies (2x + {40}^{ \circ}) + (3x - {80}^{ \circ} ) + (5x - {60}^{ \circ} ) = {180}^{ \circ}$

Finding the value of x,

$\implies 2x + {40}^{ \circ} + 3x - {80}^{ \circ} + 5x - {60}^{ \circ} = {180}^{ \circ}$

$\implies 10x - {100}^{ \circ}= {180}^{ \circ}$

$\implies 10x = {180}^{ \circ} + {100}^{ \circ}$

$\implies 10x = {280}^{ \circ}$

$\implies x = \frac{{280}^{ \circ}}{10}$

$\implies \boxed{ x = {28}^{ \circ}}$

$\large \underline{ \underline{ \text{Required Answer:}}}$

• The value of x is 28°.