Question

Two angles in a triangle are in the ratio $4:5$. If the sum of these angles is equal to the third angle, then the third angle is ___________.

• A. ${180}^o$
• B. ${40}^o$
• C. ${50}^o$
• D. ${90}^o$

Answer 1

The correct option is D ${90}^o$

Let two angles of a triangle be x,y and third angle be z.

$z=x+y$ (Given)

$x:y=4:5$ (Given)

we k.n.t sum of angles of a triangle is ${180}^{\circ }$

$x+y+z={180}^{\circ }$

$x+y+(x+y)={180}^{\circ }$

$2(x+y)={180}^{\circ }$

$x+y=\frac{{180}^{\circ }}{2}={90}^{\circ }$

Third angle $z=x+y={90}^{\circ }$