Question

Find the value of x in the figure.

Answer 1

Step-by-step explanation:

✧ $\underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \: O \: N}}}} :$

~Set up an equation and solve for x :

→ $\large{ \tt{10x + 45 \degree = 75 \degree + 70 \degree}}$ [ Exterior angle is always equal to the sum of two non-adjacent interior angles ]

Add the numbers : 75° & 70°

→ $\large{ \tt{10x + 45 \degree = 145 \degree}}$

Since we want to get rid of the constant in the left hand side , subtract 45 from both sides :

→ $\large{ \tt{10x + 45 \degree - 45 \degree= 145 \degree - 45 \degree}}$

→ $\large{ \tt{10x \: \cancel{ + 45 \degree} \: \cancel{ - 45 \degree} = 100 \degree}}$

→ $\large{ \tt{10x = 100 \degree}}$

~Divide both sides by 10

→ $\large{ \tt{ \frac{10x}{10} = \frac{100}{10}}} \degree$

→ $\large{ \tt{x = 10 \degree}}$

⟿ $\boxed{ \boxed{ \large{ \text{Our \: Final \: Answer} : \underline{ \bold{ \tt{x = 10 \degree}}}}}}$

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