Question

You want to build this bookshelf. Given that a∥ b and m∠3=x and m∠2=x+30. Find the measure of ∠4, ∠5, and ∠6

m<4= ___ Degrees
m<5= ___ Degrees
m<6= ___ Degrees

Answer 1

`\huge\boxed{m \angle 4 = 105 \textdegree}`

`\huge\boxed{m \angle 5 = 75 \textdegree}`

`\huge\boxed{m \angle 6 = 105 \textdegree}`

Explanation:

We can use basic angle relationships to find the measures of m∠4, m∠5, and m∠6.

We know that angles m∠3 and m∠2 are supplementary. This means their angle lengths add up to 180°. Since we know the expression for both, we can add them and solve for x.

• 
  `(x) + (x+30)=180`
• 
  `2x+30=180`
• 
  `2x=150`
• 
  `x = 75`

So x = 75°, aka m∠3 is 75°. This means m∠2 is going to be
`75+30=105`°.

m∠4 is an opposite angle to m∠2. This means their angle lengths are the same. Therefore, m∠4 is 105°.

We also know that m∠3 and m∠5 are alternate interior angles, meaning their angle lengths are the same. Since m∠3 is 75°, m∠5 is also 75°.

We also know that m∠6 is a corresponding angle to m∠2. This means their angle lengths are the same. Since m∠2 is 105°, m∠6 is also 105°.

Hope this helped!