Question

5. In the figure P | Q and r is a transversal. If <1 and<2 are in the ratio 3:2 determine the angles from <1 to<5?​

Answer 1

Given:-

• In the figure P | Q and r is a transversal

• <1 and<2 are in the ratio 3:2

To find :-

• Determine the angles from <1 to<5?

Solution:-

$\sf\angle1 : \angle2 = 3:2$

$\sf\angle 1 = 3x\:and \angle 2 = 2x$

$\sf Line\:t\:stands\:on\:the\:line\:P$

$\sf{\implies \angle 1 + \angle 2 = 180°\:\:\:(linear\:pair)}$

$\sf{\implies 3x + 2x = 180}$

$\sf{\implies 5x =180°}$

$\sf{\implies x =\dfrac{180°}{5}}$

$\sf{\implies x =36}$

$\sf Therefore,\: \angle 1 = 3x = 108°$

Now,

$\sf \angle\:1 = \angle 5 =\:108\:\:(Pair\:of\:corresponding\:angles)$

ㅤ ___________________

ㅤ

ㅤㅤㅤDEFINITIONS

ㅤ

Alternate Interior Angles:

These angles are formed when two || and non || are intersected by any transversal.

Vertically Opposite Angles:

These angles are vertically Opposite from each other at any vertex as in attached figure

Linear Pair Angles:

When two lines Intersect each other at any single point then two pair of angles are called linear pair.

Answer 2

Answer:

Given:-

In the figure P | Q and r is a transversal

<1 and<2 are in the ratio 3:2

To find :-

Determine the angles from <1 to<5?

Solution:-

\sf\angle1 : \angle2 = 3:2∠1:∠2=3:2

\sf\angle 1 = 3x\:and \angle 2 = 2x∠1=3xand∠2=2x

\sf Line\:t\:stands\:on\:the\:line\:PLinetstandsonthelineP

\sf{\implies \angle 1 + \angle 2 = 180°\:\:\:(linear\:pair)}⟹∠1+∠2=180°(linearpair)

\sf{\implies 3x + 2x = 180}⟹3x+2x=180

\sf{\implies 5x =180°}⟹5x=180°

\sf{\implies x =\dfrac{180°}{5}}⟹x=

5

180°

\sf{\implies x =36}⟹x=36

\sf Therefore,\: \angle 1 = 3x = 108°Therefore,∠1=3x=108°

Now,

\sf \angle\:1 = \angle 5 =\:108\:\:(Pair\:of\:corresponding\:angles)∠1=∠5=108(Pairofcorrespondingangles)

ㅤ ___________________

ㅤ

ㅤㅤㅤDEFINITIONS

ㅤ

Alternate Interior Angles:

These angles are formed when two || and non || are intersected by any transversal.

Vertically Opposite Angles:

These angles are vertically Opposite from each other at any vertex as in attached figure

Linear Pair Angles:

When two lines Intersect each other at any single point then two pair of angles are called linear pair.