Question

Given: m arc AB = 6x, m arc BC = 6x, m arc CD= x, m arc DA= 2x
Find: m < ATB

Answer 1

Answer:

m∠ATB=84°

Step-by-step explanation:

First we have to find the measure of angle ATB in terms of x

The equation would be m∠ATB=1/2(AB+DC)

Subsitute Values and you get m∠ATB=3.5x

The next step is solving for x.

Add all of the values and you get 15x. The arcs should equal 360°. This means 15x=360°

x=24° Plug it in and you get m∠ATB=84°

Answer 2

The measure of m∠ATB is 84 degrees

Circle Geometry

From the given figure, we have the following parameters

m arc AB = 6x,

m arc BC = 6x,

m arc CD= x,

m arc DA= 2x

Required parameters

m<ATB

The expression to use to get the required angle is m∠ATB=1/2(AB+DC)

Substitute the given parameters

m∠ATB=1/2(AB+DC)

m∠ATB=1/2(6x+ x)

m∠ATB=1/2(7x)

Since x = 24 degrees, hence

m∠ATB=1/2(7*24)

m∠ATB= 84 degrees

Hence the measure of m∠ATB is 84 degrees

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