Question

7. The angles of a triangle are x + 9, 6x - 6, and 9x + 1.
Find the magnitude of the three angles.
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Answer 1

Answer:

• x+9+6x-6+9x+1= 180°
• 16x+4= 180°
• 4x+1= 45
• 4x= 44
• x= 11
• x+9 =20°
• 6x-6 =66-6= 60°
• 9x+1 =99+1 =100°

Answer 2

Solution ;

Let the angles of a triangle be ∠ A , ∠B and ∠C

where ,

• ∠A = x+9
• ∠B = 6x - 6
• ∠C = 9x+1

We know that

The sum of the angles of a triangle is 180°

Then ,

∠ A+∠ B+∠C = 180°

Now , put the given values

$\sf\implies\:x+9+6x-6+9x+1=180\degree$

$\sf\implies\:(x+6x+9x)+(9-6+1)=180\degree$

$\sf\implies\:16x+4=180\degree$

$\sf\implies\:16x=180-4$

$\sf\implies\:16x=176$

$\sf\implies\:x=\dfrac{176}{16}$

$\sf\implies\:x=11$

Hence ,

• ∠A = x+9 = 20
• ∠B = 6x - 6 = 60
• ∠C = 9x+1 = 100