(30 points to best answer! ) the measure of ∠2=8x+10 and the measure of ∠4=42+6x find the measure of ∠4

Final answer is ∠4=138.

Step-by-step explanation:

Given that the measure of ∠2=8x+10 and the measure of ∠4=42+6x

Now we need to find about what is the measure of ∠4.

From given diagram we see that ∠4 and ∠2 are vertically opposite angles.

we know that vertically opposite angles are always equal so we can write:

∠4 = ∠2

8x+10 = 42+6x

8x-6x = 42-10

2x = 32

divide both sides by 2

x=16

Now plug x=16 into ∠4=42+6x to find the measure of ∠4.

∠4=42+6x =42+6*16 =42+96 =138

Hence final answer is ∠4=138.

x= 149. 24+7=31. 180-31=149

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