Question

${\bf{Theorem \: 6.4:}}$ If a transversal intersects two parallel lines then each pair of interior angles on the same side of the transversal is supplementary.

please solve it as soon as possible.​

Answer 1

${\tt{Question}}\: \purple☟$

If a transversal intersects two parallel lines then each pair of interior angles on the same side of the transversal is supplementary.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\red&#9998{\tt{Answer}}\: \orange☟$

⠀⠀$&#9679\purple{\bf{See \:the \:attachment}}\red{⇑}$

⠀ $&#9679\orange{\bf{Question\: solved}}\: \green✔$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• All necessary Formulas

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• $\orange\star{\bf{\red{\underbrace{complementary \:angle}}}}\red\star$

The sum of 2 numbers= 90

example $a−b=90°$

how to find "a" if a is not mentioned

$\red{\underbrace{\bf{\orange{Given࿐}}}}$

$a= \: ?$

$b = 40$

$a+40=\:90°$

$a=90-40°$

$a=50°$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• $\pink\star{\bf{\purple{\underbrace{supplementary\: angle}}}}\red\star$

The sum of two numbers= 180°

example= a+b=180

how to find "a" if a is not mentioned

Given

$a= \:?$

$b =\: 40$

$a+40=180°$

$a=180-40°$

$a=140°$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• $\orange\star{\bf{\green{\underbrace{Adjacent \:angle}}}}\red\star$

If there is a common ray between ${\bf&#x2220}$a and ${\bf&#x2220}$b so it is a adjacent angle.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• $\orange\star{\bf{\blue{\underbrace{Vertical\: opposite\: angle }}}}\red\star$

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

• $\orange\star{\bf{\orange{\underbrace{lenear\: pair \:of\: angles}}}}\red\star$

Here ${\bf&#x2220}$a$+{\bf&#x2220}$b$=$180°.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

Step-by-step explanation:

We know that if a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines ate parallel to each other. Hence, PQ║RS Proved. Theorem 4: If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.