Question

A and b are complementary and congruent. what is the measure of each of these angles?

Answer 1

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°.