MATH SOLVE

10 months ago

Q:
# ∠1∠1 and ∠2∠2 are a linear pair, and ∠2∠2 and ∠3∠3 are vertical angles. m∠2=(5+4y)∘m∠2=(5+4y)∘ and m∠3=(6y−25)∘m∠3=(6y−25)∘ . What is m∠1m∠1 ?

Accepted Solution

A:

Linear pair of angles ads up to 180°. Vertical angles have same value.

According to this we have:

m<1 + m<2 = 180°

m<2=m<3

We can use this to solve for m<1.

m<2=m<3

5+4y=6y-25

4y-6y=-25-5

-2y=-30

y=15

m<2=5+4*15

m<2=65°

m<1 + m<2 = 180°

m<1 + 65° = 180°

m<1 = 180° - 65°

m<1 = 115°

According to this we have:

m<1 + m<2 = 180°

m<2=m<3

We can use this to solve for m<1.

m<2=m<3

5+4y=6y-25

4y-6y=-25-5

-2y=-30

y=15

m<2=5+4*15

m<2=65°

m<1 + m<2 = 180°

m<1 + 65° = 180°

m<1 = 180° - 65°

m<1 = 115°