Sum of two angles principle is required to determined the measures of the unknown angles. So that; m∠WXZ = [tex]87^{o}[/tex] and m∠ZXY = [tex]73^{o}[/tex]
From the given question, it can be deduced that:
m<WXY = m<WXZ + m<YXZ
So that,
[tex]160^{o}[/tex] = (7x - 4) + (5x + 8)
= 7x -4 + 5x + 8
= 12x + 4
160 - 4 = 12x
156 = 12x
divide through by 12 to have;
x = [tex]\frac{156}{12}[/tex]
x = 13
The we can say;
i. m∠WXZ = (7x - 4)
= 7(13) - 4
= 91 - 4
m∠WXZ = [tex]87^{o}[/tex]
ii. m∠ZXY = (5x + 8)
= 5(13) + 8
= 65 + 8
m∠ZXY = [tex]73^{o}[/tex]
Thus, from the deductions above, m∠WXZ = [tex]87^{o}[/tex] and m∠ZXY = [tex]73^{o}[/tex].
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