Answer with explanation:
Ques 1)
We are given:
m∠B=m∠C
As we know that sides opposite to equal angles are equal.
Hence,
Length of AC=Length of AB.
i.e. x+8=2x-1
i.e. 2x-x=8+1
i.e. x=9
Also, the length of side BC is:
3x-3=3×9-3
= 27-3
= 24 units.
The value of x is: 9
Length of BC is: 24 units.
Ques 2)
As we could see that all the three angles of a triangle are equal.
Hence,
The sides opposite to equal angle are equal.
i.e.
6x-3=3x+6
i.e. 6x-3x=6+3
i.e. 3x=9
i.e. x=3
Now the length of side of BC is: 5x=5×3=15 units.
Hence,
Value of x=3
Length of BC=15 units.
Ques 3)
All the three sides of a triangle are equal.
That means:
all the three angles of a triangle are also equal.
Hence, all the angles be (7x+4)°
As we know that the sum of all the three angles of a triangle is 180 degree.
Hence,
[tex]7x+4+7x+7x+4=180\\\\\\21x+12=180\\\\\21x=168\\\\x=8[/tex]
Hence, the value of x=8
