Question

9th 2lesson 2.1
pls tell me answers pls ​

Answer 1

1st Answer

In the figure given in the answer, we are given with the extra two angles measuring 38 and 80 degree respectively. We can also observe that, a triangle has been formed in the parallel lines. So, the concept to be used here is the Angle sum property.

$\sf \dashrightarrow {Angle \: sum \: property}_{(Triangle)} = {180}^{\circ}$

$\sf \dashrightarrow {38}^{\circ} + {80}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \dashrightarrow {118}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \dashrightarrow \angle{x} = 180 - 118$

$\sf \dashrightarrow \angle{x} = {62}^{\circ}$

Hence, the value of ∠x is 62°.

2nd Answer

Now, let's find the value of x in the second figure given. Before that, we should find the value of the angle y given in the same figure.

As we can observe that, both angles having the variable u, are alternate to each other. So,

$\sf \dashrightarrow 3y = 2y + {25}^{\circ}$

$\sf \dashrightarrow 3y - 2y = 25$

$\sf \dashrightarrow 1y = 25$

$\sf \dashrightarrow y = 25$

No, we should find the value of the angle given in right side of the transversal.

$\sf \dashrightarrow 2y + 25$

$\sf \dashrightarrow 2(25) + 25$

$\sf \dashrightarrow 50 + 25$

$\sf \dashrightarrow {75}^{\circ}$

Now, we can find the value of x, as the both angles are vertically opposite to each other.

$\sf \dashrightarrow x + 15 = 75$

$\sf \dashrightarrow x = 75 - 15$

$\sf \dashrightarrow x = {60}^{circ}$

Hence, the value of ∠x is 60°.

3rd Answer

In the figure given in the answer, we have an extra two angles marked with the measurement of those angles.

We can see that there is a triangle obtained below the parallel line. So, the concept used here is the angle sum property.

$\sf \dashrightarrow {Angle \: sum \: property}_{(Triangle)} = {180}^{\circ}$

$\sf \dashrightarrow {58}^{\circ} + {80}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \dashrightarrow {138}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \dashrightarrow \angle{x} = 180 - 138$

$\sf \dashrightarrow \angle{x} = {42}^{\circ}$

Hence, the value of ∠x is 42°.