PQRS is a parallelogram. If angle P= (6x+3)° and angle Q =(4x+7)° then find the values of x and all the angles of the parallelogram
Answers
Firstly There is a Property of Parallelogram:
The consecutive Angles are supplementary ie. they add upto 180°.
Angles P&Q are consecutive so add upto 180°
hence,
P+Q=180° or
(6x+3)+(4x+7)=180
10x+10=180
10x=170
x=170/10=17°
so,
P=6*17+3=105°
Q=4*17+7=75°
R would be equal to P and S would be equal to Q
bcz opposite angles of a Parallelogram are equal.
All the angles
P= 105°
Q= 75°
R= 105°
S= 75°
Hopefully it helps✌️
Given : -
PQRS is a parallelogram .
∠P = ( 6x + 3 )°
∠Q = ( 4x + 7 )°
Required to find : -
- Value of x ?
- All angles of the parallelogram ?
Conditions used : -
Here,
Conditions refers to the properties used.
In a parallelogram ,
- Opposite angles are equal .
- Sum of two adjacent angles is supplementary .
Solution : -
PQRS is a parallelogram .
∠P = ( 6x + 3 )°
∠Q = ( 4x + 7 )°
We need to find the ;
- Value of x ?
- All angles of the parallelogram ?
So,
Now,
Let's find the value of x !
As we know that ;
In a parallelogram ,
- Sum of two adjacent angles is supplementary .
This implies ;
∠P + ∠Q = 180°
6x + 3 + 4x + 7 = 180°
10x + 10 = 180°
Take 10 common on the LHS part
10 ( x + 1 ) = 180
x + 1 = 180/10
x + 1 = 18
x = 18 - 1
x = 17
Hence,
- Value of x = 17
So,
Measurements of ∠P is ;
( 6x + 3 )°
( 6[ 17] + 3 )°
( 102 + 3 )
105°
Measurements of ∠Q is ;
( 4x + 7 )°
( 4 [ 17 ] + 7 )°
( 68 + 7 )°
75°
Hence,
- ∠ P = 105°
- ∠Q = 75°
However,
We also know that;
In a parallelogram,
- Opposite angles are equal.
This implies ;
∠P = ∠R = 105°
∠Q = ∠S = 75°
Hence,
- ∠R = 105°
- ∠S = 75°
Therefore,
Measurements of all angles are ;
105° , 75° , 105° & 75°
Verification : -
Now,
Let's verify whether our answer is correct or wrong .
So,
We know that ;
In a quadraliateral ,
Sum of all angles is equal to 360°
This implies ;
∠P + ∠Q + ∠R + ∠S = 360°
105° + 75° + 105° + 75° = 360°
180° + 180° = 360°
360° = 360°
LHS = RHS
Hence Verified !