Final Answer:
The measure of the angle is 90 degrees, and its supplementary angle measures 60 degrees.
Step-by-step explanation:
The sum of the measures of an angle and its supplementary angle is always 180 degrees. Let's denote the measure of the angle as ( A ) and its supplementary angle as ( B ). According to the given information, the measure of angle ( A ) is 150 more than the measure of its supplementary angle ( B ). This can be expressed as the equation:
[ A = B + 150 ]
Now, since the angles are supplementary, we can write another equation based on their sum being 180 degrees:
[ A + B = 180 ]
We can substitute the first equation into the second to solve for ( B ):
[ (B + 150) + B = 180 ]
Combining like terms:
[ 2B + 150 = 180 ]
Subtracting 150 from both sides:
[ 2B = 30 ]
Dividing both sides by 2:
[ B = 15 ]
Now that we know the measure of angle ( B ), we can find the measure of angle ( A ) using the first equation:
[ A = B + 150 ]
[ A = 15 + 150 = 165 ]
Therefore, the measure of the angle ( A ) is 165 degrees, and the measure of its supplementary angle ( B ) is 15 degrees.