Find the measure of each angle: ∠3 and ∠4 are supplementary. m∠3 = 5x + 22 and m∠4 = 7x + 2.

Question

25-08-2020
Mathematics

contestada

Find the measure of each angle: ∠3 and ∠4 are supplementary. m∠3 = 5x + 22 and m∠4 = 7x + 2.

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Stephen46 Stephen46 · Answer 1 · 2020-08-25T15:28:19+02:00

Answer:

∠3 = 87°

∠4 = 93°

Step-by-step explanation:

Since ∠3 and ∠4 are supplementary it means the the sum of their angles is equal to 180°

To find the angles add both ∠3 and ∠4 and equate it to 180° solve for x and substitute it into their various expressions

That's

∠3 + ∠4 = 180

5x + 22 + 7x + 2 = 180

12x + 24 = 180°

12x = 180 - 24

12x = 156

Divide both sides by 12

x = 13

So for ∠3

∠3 = 5x + 22

∠3 = 5(13) + 22

= 65 + 22

∠3 = 87°

For ∠4

∠4 = 7x + 2

∠4 = 7(13) + 2

= 91 + 2

∠4 = 93°

We have the answers as

∠3 = 87°

∠4 = 93°

Hope this helps you

TheAnimeGirl TheAnimeGirl · Answer 2 · 2020-08-25T15:37:20+02:00

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{ m \: ∠ \: 3 = 87 °}}}}[/tex]

[tex] \boxed{ \bold{\boxed{ \sf{m \: ∠4 = 93 °}}}}[/tex]

Step-by-step explanation:

We know that the sum of supplementary angle adds up to 180 °

So,

[tex] \sf{5x + 22 + 7x + 2 = 180°}[/tex]

Collect like terms

⇒[tex] \sf{12x + 22 + 2 = 180°}[/tex]

Add the numbers

⇒[tex] \sf{12x + 24 = 180°}[/tex]

Move 24 to right hand side and change it's sign

⇒[tex] \sf{12x = 180 - 24}[/tex]

Subtract 24 from 180

⇒[tex] \sf{12x = 156}[/tex]

Divide both sides of the equation by 12

⇒[tex] \sf{ \frac{12x}{12} = \frac{156}{12} }[/tex]

Calculate

⇒[tex] \sf{x = 13}[/tex]

Value of x = 13

Now, substituting / Replacing the value of x

[tex] \sf{m ∠ 3 = 5x + 22}[/tex]

⇒[tex] \sf{ m \: ∠ \: 3 = 5 \times 13 + 22}[/tex]

⇒[tex] \sf{m \: ∠ \: 3 = 65 + 22}[/tex]

⇒[tex] \sf{ \: m \: ∠ \: 3 = 87}[/tex]

Again,

[tex] \sf{ \: m \: ∠ \: 4 = 7x + 2 }[/tex]

⇒[tex] \sf{m \: ∠ \: 4 = 7 \times 13 + 2}[/tex]

⇒[tex] \sf{ \: m \: ∠ \: 4 \: = 91 + 2 }[/tex]

⇒[tex] \sf{m \: ∠ \: 4 = 93 }[/tex]

m ∠ 3 = 87

m ∠ 4 = 93

Hope I helped!

Best regards!!