How do you construct the triangle if its sides are not given and the measures of angles are 50 60 and 70 the radius of the circumcircle is 32?

Answer 1

1) Draw a circle of radius 32

2) Draw a radius (meeting the perimeter at A)

3) Based on the radius, construct an angle at the centre of the circle of 100° - draw a second radius (meeting the perimeter at B)

4) Based on the second radius, construct an angle at the centre of the circle of 120° - draw a third radius (meeting the perimeter at C)

Note : the angle between the third and first radii measures 140°.

5) Draw chords joining A to B, B to C, and C to A.

The triangle ABC has angles measuring 50°, 60° and 70°.

NOTE : The process is based on the Theorem that the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference.