Question

Р
60°
M
-
3. In the given figure, PQ is parallel
to MS and PS is the transversal.
Here ZQPS = 90° and ZPQR
60°. Find the measures of angles
1, 2, 3 and 4.
R
2.
3
4
S​

Answer 1

Answer:

1.30degree(sum of all angle in triangle is 180)

2.30degree(vertically opposite angle)

3.60degree(alternative angle)

4.90degree(alternative angle)

Step-by-step explanation:

1.angleQ+angle+angle R=180degree

60+90+angleR=180degree

150+angle R=180degree

angleR=30degree is your

thank you for your question

Answer 2

Question : -

In the given figure , PQ is || to MS and PS is a transversal . Here ∠QPS = 90° and ∠PQR = 60° . Find the measurements of ∠1 , ∠2 , ∠3 & ∠4 ?

Answer : -

Given : -

PQ || MS ( PQ is parallel to MS )

PS is a transversal .

∠QPS = 90° and ∠PQR = 60°

Required to find : -

• ∠1 , ∠2 , ∠3 & ∠4 ?

Conditions used : -

Here conditions refers to the properties , rules used .

1. Angle sum property

This states that ,

In a triangle , sum of all it's angles is equal to 180°

2. Vertically opposite angles are equal .

3. Alternate Interior angles are equal .

Solution : -

PQ || MS ( PQ is parallel to MS )

PS is a transversal .

∠QPS = 90° and ∠PQR = 60°

we need to find the values of ∠1 , ∠2 , ∠3 & ∠4 ?

So,

Consider ∆ PQR ,

In ∆ PQR

∠QPR = 90° and ∠PQR = 60°

So,

Let's find the ∠1 which is ∠PRQ .

Using the angle sum property .

∠QPR + ∠PQR + ∠PRQ = 180°

90° + 60° + ∠PRQ = 180°

150° + ∠PRQ = 180°

∠PRQ = 180° - 150°

∠PRQ = 30°

Hence,

• ∠1 = 30°

Similarly,

Now,

Consider the given information

PQ || MS ( PQ is parallel to MS )

PS is a transversal .

So,

From this we can conclude that ;

∠QPR = ∠MSR

[ Reason : Alternate Interior angles ]

This implies ;

∠MSR = 90°

Since,

∠QPR = 90°

Hence,

• ∠4 = 90°

Now,

Let's find ∠2 .

Refer to the attachment which is provided

From that we can conclude that ;

∠PRQ = ∠MRS

[ Reason : Vertically opposite angles are equal ]

So,

∠MRS = 30°

Since,

∠PRQ = 30°

Hence,

• ∠2 = 30°

Now,

Let's find the measurement of ∠3

Consider ∆ MSR

In ∆MSR ,

∠MRS = 30° & ∠MSR = 90°

So,

According to problem ;

∠MRS + ∠MSR + ∠RMS = 180°

[ Reason : Sum of all angles in a triangle is 180° ]

30° + 90° + ∠RMS = 180°

120° + ∠RMS = 180°

∠RMS = 180° - 120°

∠RMS = 60°

Hence,

• ∠3 = 60°

Therefore,

Measurements of ∠1 , ∠2 , ∠3 & ∠4 are ;

30° , 30° , 60° & 90°