Question

Answer the question attached below.....

NO SPAMMING PLS
PLS ANSWER THIS FAST

Answer 1

Answer:

hope you will understand...... if u like it then mark as brainliest.... n solving more doubts follow me..... thank you

Answer 2

${\tt{Solution \: \: (1) : }}$

We know that the angles on a straight line are called a linear pair and their measures will add up to 180°.

Sum of all the angles =180°

Measure of the first angle=40°

Measure of the second angle =4x

Measure of the third angle=3x

We can write this as an equation as:-

$= 40 + 4x + 3x = 180$

$= 40 + 7x = 180$

$= 7x = 180 - 40$

$= 7x = 140$

$= x = \frac{140}{7}$

$= x\bold{ = 20}$

Thus, the value of x=20

Which means :-

The measure of the first angle:-

$=\bold{40}°$

The measure of the second angle:-

$= 20 \times 4$

$=\bold{80}°$

Thus, the measure of the second angle =80°

The measure of the third angle:-

$= 20 \times 3$

$=\bold{60}°$

Thus, the measure of the third angle =60°

As the measure of all these angles is adding up to form 180°, we can conclude that we have found out the correct value of x.

Therefore, the value of x =20°

$\tt{Solution \: \: (2) : }$

Given :-

QP || RS

Which will mean :-

RQ is the transversal on the lines QP and RS.

Let the angle near angle ∠PQR be x .

= ∠QRS + ∠x = 180°(interior angles on the same side of transversal)

$= 130 + x = 180$

$= x = 180 - 130$

$= x = 50$

Thus, ∠x =50°

We can see that :-

∠x, ∠PQR and ∠XPQ are forming a triangle.

Which means:-

$= ∠x +∠PQR + ∠XPQ = 180°$

$= 50 + ∠PQR + ∠XPQ = 180$

∠XPQ = 180 - ∠OPQ (linear pair)

$∠XPQ = 180 - 110$

$= ∠XPQ = 70°$

So, the three angles of the triangle are=70°,50° and ∠PQR.

Then :-

$= 70 + 50 + ∠PQR = 180$

$= 120 + ∠PQR = 180$

$= ∠PQR = 180 - 120$

$= \bold{∠PQR = 60°}$

Thus, the measure of ∠PQR=60°

Therefore, the measure of ∠PQR will be=60°