The measures of two complementary angles are (14q+8)and 8q-6). Find the measures of the angles.
Two angles are complimentary if they add up to 90 degrees.
So you can say that:
(14q + 8) + (8q - 6) = 90
You can then rearrange the equation to solve for q. Then sub q back into the individual equations to calculate the angles.
14q + 8 + 8q - 6 = 90
22q + 2 = 90
22q = 88
q = 4
14q + 8 = 64
8q - 6 = 26
64 + 26 = 90
Segment EF is a midsegment of triangle ABC. If BC = 14 cm, what is the measure of segment EF
To find the measures of the two complementary angles, we need to set up an equation by equating their sum to 90°.
Let's call the first angle A and the second angle B.
According to the problem, we have the following information:
Angle A = 14q + 8
Angle B = 8q - 6
Complementary angles add up to 90°, so we can set up the equation:
Angle A + Angle B = 90°
Substituting the given values:
(14q + 8) + (8q - 6) = 90
Now, we simplify the equation and solve for q:
14q + 8 + 8q - 6 = 90
Combining like terms:
22q + 2 = 90
Next, we isolate the q variable:
22q = 90 - 2
22q = 88
Finally, we solve for q by dividing both sides of the equation by 22:
q = 88 / 22
q = 4
Now that we have found the value of q, we can substitute it back into the expressions for the angles A and B to find their measures:
Angle A = 14q + 8
Angle A = 14(4) + 8
Angle A = 56 + 8
Angle A = 64
Angle B = 8q - 6
Angle B = 8(4) - 6
Angle B = 32 - 6
Angle B = 26
So, the measure of angle A is 64 degrees, and the measure of angle B is 26 degrees.