How do you find the measures of angles G, E and F? Help pleez

m∠HDG = 28°, m∠EFG = 50°, m∠DEG = 67°, m∠DGE = 65°

Solution:

Triangle sum property:

Sum of the angles of the triangle = 180°

In ΔDHG,

m∠HDG + 120° + 32° = 180°

m∠HDG + 152° = 180°

m∠HDG = 180° – 152°

m∠HDG = 28°

In ΔGEF,

m∠EFG + 17° + 113° = 180°

m∠EFG + 130° = 180°

m∠EFG = 180° – 130°

m∠EFG = 50°

Sum of the adjacent angles in a straight line is 180°

m∠DEG + m∠DEF = 180°

m∠DEG + 113° = 180°

m∠DEG = 180° – 113°

m∠DEG = 67°

In ΔDGE,

m∠DGE + 48° + 67° = 180°

m∠DGE + 115° = 180°

m∠DGE = 180° – 115°

m∠DGE = 65°

Hence m∠HDG = 28°, m∠EFG = 50°, m∠DEG = 67°, m∠DGE = 65°.

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