contestada

Question:
Suppose on a circle that ABD is formed by a tangent and a secant intersecting outside of the circle creating the minor arcs
AC = 68° and CD = 124
1. Draw the described circle.
2. What is the measure of angle ABD

Respuesta :

calculista

Answer:

Part 1) The draw in the attached figure

Part 2) [tex]m\angle ABD=50^o[/tex]

Step-by-step explanation:

Part 1)  Draw the described circle

The draw in the attached figure

Part 2) What is the measure of angle ABD

step 1

Find the measure of arc AD

Remember that

[tex]arc\ AD+arc\ DC+arc\ AC=360^o[/tex] ----> by complete circle

substitute the given values

[tex]arc\ AD+124^o+68^o=360^o[/tex]

[tex]arc\ AD=360^o-192^o=168^o[/tex]

step 2

Find the measure of angle ABD

we know that

The measurement of the external angle is the half-difference of the arches that comprise

In this problem

The measure of angle ABD is an external angle

so

[tex]m\angle ABD=\frac{1}{2} [arc\ AD-arc\ AC][/tex]

substitute the given values

[tex]m\angle ABD=\frac{1}{2} [168^o-68^o]=50^o[/tex]

Ver imagen calculista

Otras preguntas