The values are , , and
Explanation:
It is given that and
The image having these measurements is attached below:
The angles ABC and DBE are vertically opposite.
Since, vertically opposite angles are equal,
Equating the values, we have,
Thus, the value of x is 15. Let us substitute x in the equation to find and
Thus,
Thus,
Also, substituting x = 15 in
We have,
Thus,
Hence, the measure of and
To find the measure of and :
Since, the angles in a straight line add up to 180°
To find , let us add the angles and equals to 180°
Substituting the value of DBE, we have,
Subtracting both sides by 62,
Thus, the measure of is 118°
Since, and are vertically opposite, they are equal.
Thus,
Thus, the measure of is 118°
Hence, the values of the angles are , , and