Answer:
Part 1)
Part 2)
Part 3)
Step-by-step explanation:
Part 1) Find the measure of angle ECF
we know that
CF is tangent at point C
so
the radius EC is perpendicular to the tangent CF
therefore
Part 2) Find the measure of angle AKB
we know that
The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite
substitute the values
Part 3) Find the measure of angle ACF
we know that
The inscribed angle is half that of the arc it comprises
substitute the values
Answer:
The measure of one angle is 81.3° and the other angle is 8.7°.
Step-by-step explanation:
We are given that two angles are complementary. One angle's measure is 3 more than 9 times the other angle.
Let the measure of one angle be 'x' and the measure of other angle be 'y'.
So, according to the question;
x + y = 90°
x = 90° - y ---------------- [equation 1]
x = 3 + 9y ------------ [equation 2]
Now, both the equations we get;
90 - y = 3 + 9y
9y + y = 90 - 3
10y = 87
= 8.7°
Now, putting the value of y in equation 1 we get;
x = 90° - y
x = 90° - 8.7° = 81.3°
Hence, the measure of one angle is 81.3° and the other angle is 8.7°.
