If angle A in the diagram equals 45 degrees and angle B is 4x + 5 degrees, determine the value of x.
To solve the problem, we use the fact that the sum of the angles in a triangle is 180 degrees. So, we have:
A + B + C = 180
Substituting the given values:
45 + (4x + 5) + C = 180
Simplifying:
4x + 50 + C = 180
Subtracting 50 from both sides:
4x + C = 130
But we don't know the value of angle C. However, we notice that angles A and B are acute angles (less than 90 degrees) and therefore, angle C must also be an acute angle so that it adds up to 180 degrees with the other two angles in the triangle. This means that angle C must be less than 90 degrees.
Since we know that angle B is 4x + 5 degrees and is an acute angle, we can set up an inequality:
4x + 5 < 90
Solving for x:
4x < 85
x < 21.25
Since x has to be a whole number, we round down to get:
x = 21
Therefore, the value of x is 21.