LelandNaquin
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∠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°

Respuesta :

calculista

Answer:

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°

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