In the diagram, the measure of angle 2 is 126°, the measure of angle 4 is (7x)°, and the measure of angle 5 is (4x + 4)°. What is the measure of angle 7, to the nearest degree?35°54°76°104°

Answer:The measure of angle 7 is 76°.Step-by-step explanation:If two lines intersect each other, then the alternative angles are known as vertically opposite angles.The vertically opposite angles are always congruent.From the given figure it is noticed that the angle 2 and 4 are vertically opposite angles.[tex]\angle 2=\angle 4[/tex][tex]126=7x[/tex]Divide both sides by 7.[tex]x=18[/tex]The value of x is 18.From the given figure it is noticed that the angle 5 and 7 are vertically opposite angles.[tex]\angle 5=\angle 7[/tex][tex]\angle 7=4x+4[/tex]Substitute x=18.[tex]\angle 7=4(18)+4[/tex][tex]\angle 7=72+4[/tex][tex]\angle 7=76^{\circ}[/tex]Therefore the measure of angle 7 is 76°.