Answer:
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.
