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In the diagram, the measure of angle 1 is (3x)°, and the measure of angle 2 is (12x)°.
What is the measure of angle 4?
36°
45°
135°
144°

In the diagram the measure of angle 1 is 3x and the measure of angle 2 is 12x What is the measure of angle 4 36 45 135 144 class=

Respuesta :

jennyli013
3x+12x=180
15x=180
x=12
angle 2 = angle 4
angle 4= 12x =12*(12)=144
calculista

Answer:

[tex]m<4=144\°[/tex]

Step-by-step explanation:

Step 1

Find the value of x

we know that

[tex]m<1+m<2=180\°[/tex] -----> by supplementary angles

we have

[tex]m<1=3x\°[/tex]

[tex]m<2=12x\°[/tex]

substitute and solve for x

[tex]3x+12x=180\°[/tex]

[tex]15x=180\°[/tex]

[tex]x=12\°[/tex]

Step 2

Find the measure of angle 4

we know that

[tex]m<4=m<2[/tex] -----> by vertical angles

we have

[tex]m<2=12x\°[/tex] -----> [tex]m<2=12(12)=144\°[/tex]

therefore

[tex]m<4=144\°[/tex]

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