Question

Find the m ZRTV in the figure below.

51
60
62
67

Answer 1

C 62°

Explanation:

the triangles RST and PQT are both right-angled triangles.

and we know in both triangles and additional angle.

remember, the sum of all angles in any triangle is always 180°.

so, we know in both triangles the third angles too :

180 = 90 + 23 + angle PTQ

angle PTQ = 67°

180 = 90 + 39 + angle RST

angle RST = 51°

and remember also, that the sum of all angles around a single point on one side of a line is also 180° (because they represent a half-circle with the point being the center and the line being an extended diameter).

so,

angle PTQ + angle RST + angle RTV = 180

67 + 51 + angle RTV = 180

angle RTV = 62°