Answer:
50
Step-by-step explanation:
The total of all 6 angles make a circle, which equals 360°. Using the information below the figure,
2 * m∠5 = 90°, since 2 * m∠5 = m∠1 and ∠1 is a right angle.
Because ∠1, ∠5, and ∠6 are on one side of line L, they must equal 180°, and if ∠1 equals 90°,
m∠5 + m∠6=90°.
Since 2 * m∠5=m∠1 and m∠1=90°, m∠1 must be 45°. And by Transitive Property, m∠6 also equals 90°.
If the total measure of the angles is 360° and ∠1, ∠5, and ∠6 add up to 180°, ∠2, ∠3, and ∠4 must also add to 180°.
m∠6=m∠3 - 20°. We know that m∠6 is 45°, so we put that into an equation. I am going to use x as the measure of ∠3.
45=x-20 >>> 20+45=x-20+20 >>> 20+45=x >>> 65=x >>> x=m∠3 >>> m∠3=65
m∠3=m∠4, so m∠3+m∠4=65+65, or 130. And like I said above, ∠2, ∠3, and ∠4 must add to 180°. 180 minus 130 (the measure of ∠3 + ∠4) = 50, which has to be the measure of ∠2
