Question

In the figure, angle E measures 54° and angle G measures 29°. What is the measurement of angle H?

Answer 1

∡E + ∡D = 180°
∡E = 54°             } => ∡D=180°-54°=126°

∡D+∡G+∡H=180°
∡D=126°
∡G=29°                 } => ∡H=180°-(126°+29°)=180°-155°=25°

Answer 2

From the figure, you can say that angle E is equal to angle C because they both are vertically opposite. So, you can find angle D by substracting angle E and D from 360° (sum of angles at a point) and dividing the answer by two:
360°-54°-54° = 252°
252°÷2 = 126°
Then, you can find angle H by substracting the values of angle G and angle D from 180° (sum of angles in a triangle):
180°-126°-29° = 25°
Therefore, the answer is 25°.
I hope this answered your question :)