The measure of the angle m∠CBD that forms an adjacent angle is 35 degrees.
<h3>What are adjacent angles?</h3>Adjacent angles are angles that have common side and vertex.
Therefore, the common vertex is at point B.
m∠CBD = m∠ABD - m∠ABC
Therefore,
m∠ABD = 75 degrees
m∠ABC = 40 degrees
Hence,
m∠CBD = 75 - 40
m∠CBD = 35 degrees
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Option A:
The shortest distance Mark can cover to reach home early is 54.7 miles.
Solution:
Towards North = 35 miles
Towards West = 42 miles
Using Pythagoras theorem,
<em>In right triangle, squares of the hypotenuse is equal to the sum of the squares of the other two sides.</em>
Let x be the hypotenuse.
Taking square root on both sides, we get
x = 54.67
x = 54.7
The shortest distance Mark can cover to reach home early is 54.7 miles.
Option A is the correct answer.