Question

The figure below is Circle E. Line CF is tangent at point C.

Answer 1

Answer:

Part 1) $m$

Part 2) $m$

Part 3) $m$

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

$m$

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

$m$

substitute the values

$m$

Part 3) Find the measure of angle ACF

we know that

The inscribed angle is half that of the arc it comprises

$m$

substitute the values

$m$

Answer 2

Answer:

∠ ECF = 90°

∠AKB = 77.5°

∠ACF = 75°

Step-by-step explanation:

The given figure is a circle E.

Line CF is tangent at point C.

(1) To find measures of angle ECF

Since line FC is tangent at point C and radius ECis always perpendicular to the tengent.

So ∠ ECF = 90°

(2) Measure of angle AKB

By theorem of angle formed by two interesting chords.

∠ AKB = $\frac{1}{2}$ (arc AB + arc CD)

= $\frac{1}{2}$ (50 + 105) = $\frac{1}{2}(155)$

∠AKB = 77.5°

(3) Measure of angle ACF

Since tangent chord angle = $\frac{1}{2}$ (intercepted arc)

m (∠ACF) = $\frac{1}{2}$ (m arc AB + m arc BC)

= $\frac{1}{2}(50+100)$

$\frac{1}{2}(150)$

∠ACF = 75°