Answer:
∠ABC = 62°, ∠DBE = 62°, ∠CBE = 118°, ∠ABD = 118°
Step-by-step explanation:
Solving for x
We can say that angle ABC and angle DBE are vertically opposite angles because there are only two intersecting lines. Vertically opposite angles are equal so we can form an equation:
4x + 2 = 5x - 13
5x - 4x = 2 + 13
x = 15
Angles ABC and DBE
Now we can substitute x into the equation and find out the value for angles ABC and DBE.
4(15) + 2 = 60 + 2 = 62°, just to make sure we need to substitute x into the other equation to see whether we get the same answer:
5(15) - 13 = 75 - 13 = 62°, now we can confirm that angles ABC and DBE are 62°.
Angles CBE and ABD
Now we can use the rule, angles on a straight line add up to 180°, to find the other two angles, because these two angles are vertically opposite, they are also equal to each other.
180 - 62 = 118°
Angles CBE and ABD are both 118°
