Question

∠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°

Answer 1

D. 115

Explanation:

K12 (30-question) semester test.

Answer 2

Vertical angles are opposite to each other and they are equal to each other.
Given that:
∠2 and ∠3 are vertical angles and m∠2=(5+4y)° and ​ m∠3=(6y−25)°
then
5+4y=6y-25
solving for y we get:
4y-6y=-25-5
-2y=-30
hence
y=15
thus
m∠2=(5+4y)
=5+4(15)
=5+60
=65
since ∠1 and ∠2 are linear angles, then:
∠1=180-∠2
∠1=180-65=115°