Answer:
1. The correct option is c.
2. The correct option is c.
Step-by-step explanation:
1.
From the given figure it is noticed that the angle 6 and angle 7 are lie on a straight line. It means angle 6 and 7 are supplementary angles.
The sum of supplementary angles is 180 degree.
[tex]\angle 6+\angle 7=180^{\circ}[/tex]
[tex]82^{\circ}+\angle 7=180^{\circ}[/tex]
[tex]\angle 7=180^{\circ}-82^{\circ}[/tex]
[tex]\angle 7=98^{\circ}[/tex]
Therefore option c is correct.
2.
If two lines intersect each other, then the vertically opposite angles are same.
From the given figure it is noticed that the angle 1 and 3 are vertically opposite angles, therefore measure of both angles are equal.
[tex]\angle 1=\angle 3[/tex]
[tex]2x+28=6x+4[/tex]
[tex]4x=24[/tex]
[tex]x=6[/tex]
The value of x is 6.
The measure of angle 3 is
[tex]\angle 3=6(6)+4[/tex]
[tex]\angle 3=40^{\circ}[/tex]
Therefore option c is correct.
The measure of angle 7 is 98 degrees
the measure of m∠3 is 40 degrees
Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. Corresponding angles are equal.
Therefore,
m∠2 ≅ m∠6
The measure of f m∠7 can be found as follows:
m∠7 = 180 - 82 = 98° (angle on a straight line)
m∠1=(2x+28) and m∠3=(6x+4) are vertically opposite angle .
Vertical angles share the same vertex and are formed by intersecting lines. Vertical angles are equal. Therefore,
2x + 28 = 6x + 4
28 - 4 = 6x - 2x
24 = 4x
x = 24 / 4
x = 6
Therefore,
m∠3 = 6(6) + 4 = 40°
learn more on angles here: https://brainly.com/question/1537734
