Question

What is the measure of Arc BA? An explanation would be much appreciated.

Answer 1

The measure of arc BA is determined as 140⁰ (Option D).

How to calculate the measure of arc BA?

The measure of arc BA is calculated by applying the following formula as shown below;

The value of arc CB is calculated as;

arc CB = 2 x m∠CDB

arc CB = 2 (2z + 4)

arc CB + CD = 180 (sum of angles in a semi circle)

2 (2z + 4) + 16z + 12 = 180

4z + 8 + 16z + 12 = 180

20z + 20 = 180

20z = 160

z = 160 / 20

z = 8

arc CB = 2 (2 x 8 + 4)

arc CB = 40

arc AD = arc CB = 40

arc CD = 16 z + 12

arc CD = (16 x 8) + 12

arc CD = 140

The measure of arc BA is calculated as;

arc BA = 360 - ( arc CB + arc CD + arc AD)

arc BA = 360 - ( 40 + 140 + 40)

arc BA = 140⁰

Answer 2

m<BA = 180degrees

Explanation:

First you must know that measure of <BA is 180 degrees and m<CD = m<BA

Since <CD = 16z - 12, hence;

180 = 16z - 12

16z = 180++12

16z = 192

z = 192/16

z = 12

Get <BA

m<BA = 16z - 12

m<BA = 16(12) - 12

m<BA = 192 - 12

m<BA = 180degrees