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

.

what is m∠1

?

65°
85°
95°
115°

The measure of angle 1 is 115°

Step-by-step explanation:

we know that

If ∠1 and ∠2 are a linear pair

then

∠1 +∠2 =180° > supplementary angles

If ∠2 and ∠3 are vertical angles

then

∠2 =∠3

step 1

Find the value of y

we know that

∠2 =∠3

substitute values

(5+4y)°=(6y-25)°

6y-4y=(5+25)°

2y=(30)°

y=15°

step 2

Find the measure of angle 2

∠2=(5+4y)°

substitute the value of y

∠2=(5+4(15))°

∠2=65°

step 3

Find the measure of angle 1

we know that

∠1 +∠2 =180°

we have

∠2=65°

substitute

∠1 +65°=180°

∠1 =180°-65°=115°

he answer is x=1x3 because x=1 to x=3