The measure of arc AD is 116 degrees and it can be determined by using the properties of a circle.
Given that,
Angle ABD measures (4x + 10).
Angle ACD measures (5x − 2).
Circle E is shown.
Angles ABD and ACD intercept arc AD.
Angles BAC and BDC intercept arc BC.
We have to determine,
What is the measure of arc AD?
According to the question,
Angle ABD measures (4x + 10).
Angle ACD measures (5x − 2).
Circle E is shown.
Angles ABD and ACD intercept arc AD.
Angles BAC and BDC intercept arc BC.
In the given condition, Angle ABD and Angle ACD have inscribed angles, intercepting the same arc then by the intercept arc property.
Angle ABD = Angle ACD
[tex]\rm 4x+10 = 5x-2\\\\4x-5x = -2-10\\\\-x = -12\\\\x=12[/tex]
The value of x is 12.
Therefore,
The measure of arc AD is,
[tex]\rm Arc \ AD =A ngle \ ABD + Angle \ ACD\\\\Arc \ AD = (4x+10) + (5x-2)[/tex]
Substitute the value of x,
[tex]\rm Arc \ AD = (4x+10) + (5x-2)\\\\Arc \ AD = 4(12) +10+5(12) -2\\\\Arc \ AD = 48+10+60-2\\\\Arc \ AD = 116 \ degree[/tex]
Hence, the measure of arc AD is 116 degrees.
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https://brainly.com/question/9929636
