Question

The question is in the picture please explain.

Answer 1

Answer:

x = 78

Step-by-step explanation:

Look at Triangle DBH. Two of its angles are known. Let y = <DHB

47 + 31 + y  = 180        All triangles have 180 degrees. Combine the left.

78 + y = 180                Subtract 78 from both sides.

78-78+y = 180-78        Combine

y = 102

Notice that y + x = 180   They form a straight line.

102 + x = 180                   Subtract 102 from both sides.

x = 78

You should notice that x is an exterior angle. (I didn't at first).

Exterior angles are the sum of the two remote interior angles which in this case, are 31 + 47 = 78

Much shorter and much easier.