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Answer: x = 62.5 degrees
Step-by-step explanation:
Angle DEC is adjacent to the angle measuring 137 degrees, which means their sum is 180 degrees. Therefore:
Angle DEC + 137 = 180
We can subtract 137 from both sides:
Angle DEC = 43 degrees
We know that the sum of the angles in a triangle is 180 degrees, so we can set up an equation for triangle DEC.
We know Angle D + Angle C + Angle E = 180, so we can plug in the values given for each.
Therefore, x + 5 + x + 7 + 43 = 180
We can combine like terms:
2x + 55 = 180
Subtract 55 from both sides:
2x = 125
Divide both sides by 2:
x = 62.5 degrees