Question

What is the measure of angle X?

Answer 1

Answer: 71 degrees

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Step-by-step explanation:

Focus on triangle BDH

Interior angles B and D are given to be 40 and 31 respectively. Interior angle H is unknown

For any triangle, the interior angles always add to 180

B+D+H = 180

40+31+H = 180

H+71 = 180

H = 180-71

H = 109

Interior angle H is 109 degrees for triangle BDH

The exterior angle is 180 minus this measure

exterior angle = 180 - (interior angle)

exterior angle = 180 - 109

exterior angle = 71

Note how this is the sum of interior angles B and D, so you could use the remote interior angle theorem here.

Answer 2

The measure of angle X is 71 degrees.

Focusing on triangle BDH, given interior angles B and D as 40 and 31 degrees, respectively, and labeling the unknown interior angle as H, we apply the fact that the sum of interior angles in any triangle is always 180 degrees. Setting up the equation B+D+H=180, substituting the given values, we find 40+31+H=180. Simplifying, we isolate H and determine that the interior angle H in triangle BDH is 109 degrees.

To find the exterior angle, we use the relationship between interior and exterior angles, subtracting the interior angle from 180. Therefore, the exterior angle is 180−109=71 degrees, which interestingly matches the sum of interior angles B and D. This alignment demonstrates the application of the remote interior angle theorem.