Question

please answer this fast​

Answer 1

• Value of x is 15°

Step-by-step explanation:

To find:-

• Value of x.

Solution:-

Given that,

AB and CD are parallel lines. And t is transversal.

We know,

Sum of two adjacent interior angles, when parallel lines interest by an transversal is 180°. We also say this statement be $\sf \blue{Co-interior \: angles}.$

So,

$\sf \longrightarrow 4x + 7 + 7x + 8 = 180 \degree$

$\sf \longrightarrow 11x + 15 = 180\degree$

$\sf \longrightarrow 11x = 180\degree - 15$

$\sf \longrightarrow 11x = 165\degree$

$\sf \longrightarrow x = \dfrac{165\degree}{11}$

$\longrightarrow \purple{\boxed{\sf \bold{x = 15\degree}} \star}$

Verification:-

$\sf \longrightarrow (4x + 7)+(7x + 8) = 180\degree$

• $\sf Put \: x = 15\degree$

$\sf \longrightarrow \bigg( 4 \times (15\degree) + 7\bigg) + \bigg( 7 \times (15\degree) + 8 \bigg) = 180\degree$

$\sf \longrightarrow (60 \degree + 7) + (105 \degree + 8) = 180\degree$

$\sf \longrightarrow 67 \degree + 113 \degree = 180\degree$

$\sf \longrightarrow 180 \degree = 180\degree$

$\boxed{\sf Hence \: Verified.}$

Therefore,

Value of x is 15°.

_________________

Let, Read more about some properties when two parallel lines interest by an transversal and Of straight line.

• Alternative interior angles are equal.

• Sum of all angles forms on straight line is 180° or linear pair.

• Corresponding angles are equal.

• Vertically opposite angles are equal.

Answer 2

Answer:

Given :-

• AB and CD are parallel line.
• T is transversal.
• Distance between A and t is 7x + 8
• Distance between C and t is 4x + 7

To Find :-

Value of x

SoluTion :-

As we know that,

Sum of two adjacent interior angles, when parallel lines interest by an transversal is 180.

So,

$\sf \implies \: 4x + 7 + 7x + 8 = 180$

$\sf \implies \: 11x + 15 = 180$

$\sf \implies \: 11x = 180 - 15$

$\sf \implies \: 11x = 165$

$\sf \implies \: x \: = 165 \div 11$

$\sf \implies \: x = 15$

Let's verify

$\sf \: 4x + 7 + 7x + 8 = 180$

$\sf \: 4 \times 15 + 7 + 7 \times 15 + 8 = 180$

$\sf \: 60 + 7 + 105 + 8 = 180$

$\sf \: 67 + 113 = 180$

$\sf \: 180 = 180$