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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

You want to build this bookshelf Given that a b and m3x and m2x30 Find the measure of 4 5 and 6 mlt4 Degrees mlt5 Degrees mlt6 Degrees class=

Respuesta :

thepingu

Answer:

[tex]\huge\boxed{m \angle 4 = 105 \textdegree}[/tex]

[tex]\huge\boxed{m \angle 5 = 75 \textdegree}[/tex]

[tex]\huge\boxed{m \angle 6 = 105 \textdegree}[/tex]

Step-by-step 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.

  • [tex](x) + (x+30)=180[/tex]
  • [tex]2x+30=180[/tex]
  • [tex]2x=150[/tex]
  • [tex]x = 75[/tex]

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

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!