Question

If the radian measures of two angles of a triangle are as given below. Find the radian measure and the degree measure of the third angle.
(i) $\frac{5\pi }{9},\frac{5\pi }{18}$
(ii) $\frac{3\pi }{5},\frac{4\pi }{15}$

Answer 1

We have,

Part (i). $\frac{5\pi }{9},\frac{5\pi }{18}$

Part (ii). $\frac{3\pi }{5},\frac{4\pi }{15}$

Let the third angle of triangle$=x$

Then, we know that

Angle sum property of a triangle

Solve Part (i).

$\frac{5\pi }{9}+\frac{5\pi }{18}+x=\pi$

$\frac{10\pi +5\pi }{18}+x=\pi$

$x=\pi -\frac{15\pi }{18}$

$x=\pi -\frac{5\pi }{6}$

$x=\frac{6\pi -5\pi }{6}$

$x=\frac{\pi }{6}$

$x=\frac{{180}^o}{6}$

$x={30}^o$

Solve Part (ii).

$\frac{3\pi }{5}+\frac{4\pi }{15}+x=\pi$

$\frac{9\pi +4\pi }{15}+x=\pi$

$x=\pi -\frac{13\pi }{15}$

$x=\frac{15\pi -13\pi }{15}$

$x=\frac{2\pi }{15}$

$x=\frac{2\times {180}^o}{15}$

$x=2\times {12}^o$

$x={24}^o$

Hence, this is the answer.