Given, in the figure PR and PS are two tangents. They meet at P. Here angle P given. ∠P = 42°.
If we take a straight line PQ, it will create two triangles.
We can see here angle R and angle S both are right angles.
As here two triangles, so sum of all the angles of the triangles is [tex] 180^o + 180^o = 360^o [/tex]
Now if we subtract the two right angles we will get,
[tex] 360^o-90^o-90^o = 360^o-180^o = 180^o [/tex]
That means ∠P+∠Q = 180°
If we substitute the value of angle P we will get,
[tex] 42^o+Q = 180^o [/tex]
We can get angle Q by subtracting 42 to both sides. We will get,
[tex] 42^o+Q-42^o = 180^o-42^o [/tex]
[tex] Q = 180^o-42^o [/tex]
[tex] Q = 138^o [/tex]
So we have got angle Q, the measurement of ∠Q = 138°.
