Based on the definition of isosceles triangle, the value of x in the given diagram is: 84°.
What is an Isosceles Triangle?
An isosceles triangle has two base angles of equal length.
Given that, a = 22°, and using the information in the image attached below, we have the following:
m∠1 = a = 22° (base angles)
m∠2 = a + m∠1 = 22 + 22 = 44° (external angle theorem)
m∠3 = m∠2 =44° (base angles)
m∠4 = 180 - (180 - m∠2 - m∠3) - m∠1 = 180 - (180 - 44 - 44) - 22
m∠4 = 70°
m∠5 = m∠4 = 70° (base angles)
m∠6 = 180 - (180 - m∠5 - m∠4) - m∠3
m∠6 = 180 - (180 - 70 - 70) - 44
m∠6 = 96°
m∠7 = m∠6 = 96° (base angles)
x = 180 - m∠7
x = 180 - 96
x = 84°
Therefore, based on the definition of isosceles triangle, the value of x in the given diagram is: 84°.
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