Question

Two angles of a triangle are `(5pi^"c")/9` and `(5pi^"c")/18`. Find the degree and radian measures of third angle.

Answer 1

We know that θ^c = [θ x]° The measure of two angles of a triangle are [latex] `(5pi^c)/9, (5pi^c)/18`,

i.e., `((5pi)/9 xx 180/pi)^circ"," ((5pi)/18 xx 180/pi)^circ`

i.e., 100°, 50°

Let the measure of third angle of the triangle be x°.

∴ 100° + 50° + x° = 180°   …[Sum of the angles of a triangle is 180°.]
∴ x° = 180° – 100° – 50°
∴ x° = 30°

= `(30 xx pi/180)^c   ....[∵ theta xx pi/180]^c`

= `(pi/6)^c`

∴ The degree and radian measures of the third angle are 30° and `(π/6)^c` respectively.