Question

# Given: triangleGRA angleGRA=85^circ angleRGA=63^circ angleRAG=?^circ

Solid Geometry
Given:
$$\displaystyle\triangle{G}{R}{A}$$
$$\displaystyle\angle{G}{R}{A}={85}^{\circ}$$
$$\displaystyle\angle{R}{G}{A}={63}^{\circ}$$
$$\displaystyle\angle{R}{A}{G}=?^{\circ}$$

From the triangle angle sum theorem, we know that the sum of all angles of a triangle must be equal to $$180^{\circ}$$. Let $$\displaystyle\angle{R}{A}{G}$$ be x.
$$\displaystyle{x}+{85}^{\circ}+{63}^{\circ}={180}^{\circ}$$
$$\displaystyle{x}={180}^{\circ}-{85}^{\circ}-{63}^{\circ}$$
$$\displaystyle{x}={32}^{\circ}$$