Question

in the given figure l is parallel to m and t is a transversal. If angle 1 and angle 2 are 8n ratio of 5:7, find the measure of each of the angles:

angle 1
angle 2
angle 3
angle 8​

Answer 1

Answer:

angle 1 = angle 3 =75

angle 2=angle 4 =105

Step-by-step explanation:

angle 1 + angle 2 = 180 [linear pair axiom]

5x +7x =180

12x =180

x= 180/12

x=15

therefor; angle 1 = 5x= 5 X 15= 75

and; angle 2 = 7x = 7 X 15 = 105

angle 1 = angle 3 =75  [vertically opp. angles]

angle 2=angle 4 =105 [vertically opp. angles]

Answer 2

ANSWER : $\angle {1} = {75°}$ $\angle {2} ={105°}$ $\angle {3} = {75°}$ $\angle {8} = {105°}$

$\boxed {\boxed {\large {\mathbb{Solution :}}}}$

Ratio of $\angle {1}$ and $\angle {2}$ is 5:7

Let common factor be x.

So,

Angle 1 = 5x, Angle 2 = 7x

Now,

7x + 5x = 180°

=> 12x = 180°

=> x = $\dfrac {180°}{12}$

=> x = 15°

________________

[ Put the value of x in angle 1 & angle 2 ]

$\angle {1} = {5} × {15} = {75°}$

$\angle {2} = {7} × {15} = {105°}$

♦ $\angle {1} = \angle {3} = 75°$ -- (Vertically Opposite angles )

♦ $\angle {2} = \angle {6} = {105°}$ --(Corresponding angles )

♦ $\angle {6} = \angle{8} = {105°}$ -- (Vertically Opposite angle).

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$\bf {Thanks:)}$