Question

If three angles in a triangle are a -x^2, b-x+40, and c-x+60, what is angle c?

Answer 1

Explanation:

x²+X+60+X+40=180 [sum of angles of ∆]

or,x²+2x+100-180

or,x²+2x-80=0

or,x²+10x-8x-80=0

or,x(x+10)-8(x+10)=0

or,(x-8)(x+10)=0

Either,. OR,

X=8. x=-10

when,x=8 then <A=(8)²=64°,<B=8+40=48°,<C=8+60=68°

When,x=-10 then

<A=(-10)²=100°,<B=-10+40=30°,<C=-10+60=50°

Answer 2

• Angle C is 68° (or 50°)

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According to angle sum property the sum of three interior angles is 180°.

Set equation and solve for x:

• x² + x + 40 + x + 60 = 180
• x² + 2x + 100 = 180
• x² + 2x = 80
• x² + 2x + 1 = 81
• (x + 1)² = 81
• x + 1 = ± 9
• x = 8 or x = - 10

Angle C is:

• 8 + 60 = 68° or
• -10 + 60 = 50°