Question

In the given figure all b with t as transversal . Find the value of x​ , plz help me

Answer 1

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

• In the given figure all b with t as transversal . Find the value of x.

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

As given,

• $\text{Line} \: a \parallel \text{Line} \: b.$

And,

• $\text{Line} \: t \: \text{is transversal to line} \: a \text{ and }b.$

As we know that,

• The angles made in interior by a transversal are supplementary angles.

We get,

$\cdot \cdot \cdot\longrightarrow (6x + {7}^{ \circ} ) + (3x + {38}^{ \circ} ) = {180}^{ \circ}$

Opening the brackets,

$\cdot \cdot \cdot\longrightarrow 6x + {7}^{ \circ} + 3x + {38}^{ \circ} = {180}^{ \circ}$

Collecting all same unit terms separately,

$\cdot \cdot \cdot\longrightarrow 6x + 3x + {7}^{ \circ} + {38}^{ \circ} = {180}^{ \circ}$

We find,

$\cdot \cdot \cdot\longrightarrow 9x + {45}^{ \circ} = {180}^{ \circ}$

$\cdot \cdot \cdot\longrightarrow 9x = {180}^{ \circ} - {45}^{ \circ}$

$\cdot \cdot \cdot\longrightarrow 9x = {135}^{ \circ}$

$\cdot \cdot \cdot\longrightarrow x = \frac{ {135}^{ \circ}}{9}$

Therefore,

$\cdot \cdot \cdot\longrightarrow \large \boxed{ x = {15}^{ \circ}}$

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

• The value of x is 15°.