A and b are complementary and congruent. what is the measure of each of these angles?
Answer: The required measures of angles A and B is 45°.
Step-by-step explanation: Given that the angles A and B are complementary and congruent.
We are to find the measure of angles A and B.
Let x and y represents the measures of angles A and B respectively in degrees.
According to the given information, we have
\(x+y=90^\circ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x=y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\)
From equations (i) and (ii), we get
\(x+x=90^\circ\\\\\Rightarrow 2x=90^\circ\\\\\Rightarrow x=\dfrac{90^\circ}{2}\\\\\Rightarrow x=45^\circ.\)
Therefore, from equation (ii), we get
\(x=y=45^\circ.\)
Thus, the required measures of angles A and B is 45°.