Question

Given that < DAB and < DCB are right angles and m < DBC = 42, what is the measure of CAB

Answer 1

Please consider the attached diagram.

We have been given that angle DAB and angle DCB are right angles. We are also told that measure of angle DBC is 42 degrees. We are asked to find the measure of arc CAB.  

We can see that angle DBC is inscribed angle of arc DC, so measure of arc DC is two times the measure of angle DBC.

$\widehat{DC}=42^{\circ}\times 2=84^{\circ}$

We can also see that segment DB is diameter of given circle as inscribed angle of diameter is a right angle.

Since segment DB is diameter of given circle, so measure of arc DAB would be equal to half the measure of 360 degrees.

$\widehat{DAB}=\frac{360^{\circ}}{2}=180^{\circ}$

$\widehat{CAB}=\widehat{CD}+\widehat{DAB}$

$\widehat{CAB}=84^{\circ}+180^{\circ}$

$\widehat{CAB}=264^{\circ}$

Therefore, the measure of arc CAB is 264 degrees.