Question

Match the following items.

Answer 1

Answer:

1. ∠ABD = 20°.

2.  Arc AB =  140°.

3.  Arc AD =  40°.

Step-by-step explanation:

Given information: ∠ADB = 70°. BD is diameter.

According to Central angle theorem, the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points.

By Central angle theorem,

$\angle DAB=90^{\circ}$

Using angle sum of property in triangle ADB we get,

$\angle ADB+\angle DAB+\angle ABD=180^{\circ}$

$70^{\circ}+90^{\circ}+\angle ABD=180^{\circ}$

$\angle ABD=20^{\circ}$.

Draw a line segment AO.

In triangle AOD, AO=OD, so

$\angle ODB=\angle OAD=70^{\circ}$

Using angle sum property in triangle AOD,

$\angle AOD+\angle ODA+\angle OAD=180^{\circ}$

$\angle AOD+70^{\circ}+70^{\circ}=180^{\circ}$

$\angle AOD=40^{\circ}$

Therefore length of arc AD is 40°.

The angle AOD and AOB are supplementary angles.

$\angle AOD+\angle AOB=180^{\circ}$

$40^{\circ}+\angle AOB=180^{\circ}$

$\angle AOB=140^{\circ}$

Therefore length of arc AB is 140°.