Respuesta :

Answer:

D) 91°

Step-by-step explanation:

From the figure we can write the angle relationship as follows:

[tex]m\angle 1=m\angle 3[/tex]      [Vertical angles are congruent]

[tex]m\angle 2=m\angle 4[/tex]      [Vertical angles are congruent]

[tex]m\angle 2+m\angle 3=180\°[/tex]      [Linear pair of angles have sum = 180°]

We are given:

[tex]m\angle 2=5x+14[/tex]

[tex]m\angle 3=7x-14[/tex]

We know, [tex]m\angle 2+m\angle 3=180\°[/tex]

So, we have:

[tex]5x+14+7x-14=180[/tex]

Solving for [tex]x[/tex]

Combining like terms

[tex]12x=180[/tex]

Dividing both sides by 12.

[tex]\frac{12x}{12}=\frac{180}{12}[/tex]

[tex]x=15[/tex]

Using [tex]x=15[/tex] to evaluate ∠3

[tex]m\angle 3 = 7(15)-14=105-14=91\°[/tex]

We know [tex]m\angle 1=m\angle 3[/tex]

∴ [tex]m\angle 1=91\°[/tex]  (Answer)

AnswarMay

Answer:

91

Step-by-step explanation:

From the figure we can write the angle relationship as follows:

m\angle 1=m\angle 3m∠1=m∠3 [Vertical angles are congruent]

m\angle 2=m\angle 4m∠2=m∠4 [Vertical angles are congruent]

$m\angle 2+m\angle 3=180\°$ [Linear pair of angles have sum = 180°]

We are given:

$m\angle 2=5x+14$

$m\angle 3=7x-14$

We know, $m\angle 2+m\angle 3=180\°$

So, we have:

$5x+14+7x-14=180$

Solving for $x$

Combining like terms

$12x=180$

Dividing both sides by 12.

$\frac{12x}{12}=\frac{180}{12}$

$x=15$

Using $x=15$ to evaluate ∠3

$m\angle 3 = 7(15)-14=105-14=91\°$

We know $m\angle 1=m\angle 3$

∴ $m\angle 1=91\°$ (Answer)

Otras preguntas