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∠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 ?

Respuesta :

Rodiak
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°
boffeemadrid

Answer:

[tex]{\angle}1=115^{\circ}[/tex]

Step-by-step explanation:

It is given that the ∠1 and ∠2 forms a linear pair and ∠2 and ∠3 are the vertical angles.

Also, we are given that the measure of the ∠2 is ∠2=(5+4y)° and the measure of ∠3 is ∠3=(6y-25)°.

Since, ∠2 and ∠3 forms vertical angles, thus they will be equal in measure, hence

[tex]{\angle}2={\angle}3[/tex]

⇒[tex](5+4y)^{\circ}=(6y-25)^{\circ}[/tex]

⇒[tex]5+25=6y-4y[/tex]

⇒[tex]30=2y[/tex]

⇒[tex]y=15^{\circ}[/tex]

Therefore, the measure of ∠2 will be:

[tex]{\angle}2=5+4(15)=5+60=65^{\circ}[/tex]

Now, ∠1 and ∠2 forms linear pair, therefore

[tex]{\angle}1+{\angle}2=180^{\circ}[/tex]

⇒[tex]{\angle}1+65^{\circ}=180^{\circ}[/tex]

⇒[tex]{\angle}1=115^{\circ}[/tex]

Hence, the measure of ∠1 is [tex]115^{\circ}[/tex].

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