The answer is -5. Just plug in -5 to check and x will equal 3.
Answer:
See below ~
Step-by-step explanation:
<u>Given</u> : 3 angles of a Δ
- (x + 5)°
- (x + 10)°
- (x + 15)°
<u>Solving</u> :
- According to Angle Sum Property of a triangle, the angles of a triangle add up to 180°
- x + 5 + x + 10 + x + 15 = 180
- 3x + 30 = 180
- x + 10 = 60
- x = 50
<u>Finding the angles</u>
- x + 5 = 50 + 5 = 55°
- x + 10 = 50 + 10 = 60°
- x + 15 = 50 + 15 = 65°
The given equation is-

First, we move the independent term to the other side.

Now, we have to use the quadratic equation to find the solutions.-
![x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x_%7B1%2C2%7D%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Where, a = 1, b = -10, and c = 34.
Replacing these values in the formula, we have.
![\begin{gathered} x_{1,2}=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(1)(34)}}{2(1)} \\ x_{1,2}=\frac{10\pm\sqrt[]{100-136}}{2}=\frac{10\pm\sqrt[]{-36}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x_%7B1%2C2%7D%3D%5Cfrac%7B-%28-10%29%5Cpm%5Csqrt%5B%5D%7B%28-10%29%5E2-4%281%29%2834%29%7D%7D%7B2%281%29%7D%20%5C%5C%20x_%7B1%2C2%7D%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B100-136%7D%7D%7B2%7D%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B-36%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
But, there's no square root of -36 because it's a negative. To solve this issue, we use complex numbers that way, we would have solutions.
![x_{1,2}=\frac{10\pm\sqrt[]{36}i}{2}=\frac{10\pm6i}{2}=5\pm3i](https://tex.z-dn.net/?f=x_%7B1%2C2%7D%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B36%7Di%7D%7B2%7D%3D%5Cfrac%7B10%5Cpm6i%7D%7B2%7D%3D5%5Cpm3i)
<h2>Therefore, the solutions are</h2>

The right answer is B.
Answer:
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