Question

do now #10: what type of angles? find the value of x: 3x + 20 5x - 8 what type of angles? find the value of x: 8x + 5 10x - 7 what type of angles? find the value of x: 5x - 22 2x + 20 what type of angles? find the value of x: 7x - 30 3x + 14

Explanation:

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Step1: Identify angle type

The angles $3x + 20$ and $5x-8$ are alternate - interior angles (formed by a transversal cutting two parallel lines and are on the inside of the parallel lines and opposite sides of the transversal).

Step2: Set up equation

Since alternate - interior angles are equal, we set up the equation $3x + 20=5x - 8$.

Step3: Solve for x

Subtract $3x$ from both sides: $20 = 5x-3x - 8$, which simplifies to $20 = 2x-8$. Then add 8 to both sides: $20 + 8=2x$, so $28 = 2x$. Divide both sides by 2: $x = 14$.

Step1: Identify angle type

The angles $8x + 5$ and $10x-7$ are corresponding angles (formed by a transversal cutting two parallel lines and are in the same relative position).

Step2: Set up equation

Since corresponding angles are equal, we set up the equation $8x + 5=10x - 7$.

Step3: Solve for x

Subtract $8x$ from both sides: $5 = 10x-8x - 7$, which simplifies to $5 = 2x-7$. Add 7 to both sides: $5 + 7=2x$, so $12 = 2x$. Divide both sides by 2: $x = 6$.

Step1: Identify angle type

The angles $5x-22$ and $2x + 20$ are vertical angles (opposite angles formed by the intersection of two lines).

Step2: Set up equation

Since vertical angles are equal, we set up the equation $5x-22=2x + 20$.

Step3: Solve for x

Subtract $2x$ from both sides: $5x-2x-22=20$, which simplifies to $3x-22 = 20$. Add 22 to both sides: $3x=20 + 22$, so $3x = 42$. Divide both sides by 3: $x = 14$.

Answer:

Type of angles: Alternate - interior angles. Value of $x$: $14$

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