Question

In the given figure, l || m and a transversal t cuts them. If ∠1:∠2 =5:4, find the measure of each of the marked angles.​

Answer 1

Answer:

It is given that ∠1=120

o

from the figure we know that ∠1 and ∠2 form a linear pair of angles

so it can be written as

∠1+∠2=180

o

by substituting the values

120

o

+∠2=180

o

∠2=60

o

from the figure we know that ∠1 and ∠3 are vertically opposite angles

we get

∠1=∠3=120

o

from the figure we know that ∠2 and ∠4 are vertically opposite angles

we get

∠2=∠4=60

o

it is given that l∥m and t is a transversal

so the corresponding angles according to the figures is written as

∠1=∠5=120 °

∠2=∠6=60 °

∠3=∠7=120 °

∠4=∠8=60 °

pls follow me

Answer 2

$\huge{\underline{\underline{\sf{\orange{</p><p>Question:-}}}}}$

In the given figure, l || m and a transversal t cuts them. If ∠1:∠2 =5:4, find the measure of each of the marked angles.

$\huge{\underline{\underline{\sf{\orange{</p><p>Solution:-}}}}}$

Let ∠1 = (5x)° and ∠2 = (4x)°.

clearly, the ray t stands on line l .

$\therefore \: \angle \: 1 + \angle \: 2 = 180\degree \: ⇒ 5x + 4x = 180 \\ ⇒ 9x = 180 ⇒ x = 20.$

$\therefore \: \angle \: 1 = (5 \times 20)\degree = 100\degree \: and \: \angle \: 2 = (4 \times 20)\degree = 80\degree.$

$now \: \angle \: 3 = \angle \: 1 = 100\degree \\ \angle 4 = \angle \: 2 = 80\degree$

$now \: l || m \: and \: t \: is \: the \: transversal.$

$\therefore \: \angle \: 5 = \angle \: 3 = 100\degree \\ \angle \: 6 = \angle \: 4 = 80\degree \\ \angle \: 7 = \angle \: 3 = 100\degree \\ \angle \: 8 = \angle \: 4 = 80\degree$

$\therefore \: \angle \: 1 = 100\degree, \: \angle \: 2 = 80\degree, \: \angle \: 3 = 100\degree, \: \angle \: 4 = 80\degree, \\ \angle \: 5 = 100\degree, \: \angle \: 6 = 80\degree, \: \angle \: 7 = 100\degree, \: \angle \: 8 = 80\degree$