Answer: m∠1=42°
Step-by-step explanation
For this problem, we can separate the triangle into 2 separate triangles to solve for m∠1.
We know that m∠4 is 106°. ∠2 and ∠4 are supplementary angles. You can see that they make a straight line of 180°. We can use this fo find ∠2.
∠2+∠4=180
∠2+106=180
∠2=74°
Now that we know ∠2 is 74°, we can use that to solve for m∠1.
We know that the measures of the angles in a triangle equal to 180°. For the triangle at the bottom, we see ∠3, ∠2, ∠1. Since we know ∠3 and ∠2, we can find ∠1.
∠3+∠2+∠1=180
64+74+∠1=180
138+∠1=180
∠1=42°
