Answer: 93 degrees
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Step-by-step explanation:
Let x be the question mark angle we want to find.
Let y be adjacent to the 127 degree angle
Let z be adjacent to the 146 degree angle.
Refer to the diagram below.
Note that in the diagram, I have a second copy of 'x' because the two x angles are vertical angles. Vertical angles are always congruent.
Let's find angle y
127+y = 180
y = 180-127
y = 53
Do the same for angle z
z+146 = 180
z = 180-146
z = 34
Then notice how,
x+y+z = 180
x+53+34
x+87 = 180
x = 180-87
x = 93