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lukerothbacher
13.01.2021 •
Mathematics
6.1 Practice Assignment
Solve for x and find the measure of ZWZX? please help!
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Ответ:
x = 56
m∠WZX = 51°
Step-by-step explanation:
The measure of the exterior angle at a vertex of a triangle equal to the sum of the measures of the two opposite interior angles to this vertex
In ΔWZX
∵ The angle of measure 148° is an exterior angle at vertex x
∵ ∠XWZ and ∠WZX are the opposite interior angles to vertex X
→ By using the rule above
∴ m∠XWZ + m∠WZX = 148°
∵ m∠XWZ = (2x - 15)°
∵ m∠WZX = (x - 5)°
→ Substitute them in the equation above
∴ 2x - 15 + x - 5 = 148
→ Add the like terms on the right side
∵ (2x + x) + (-15 - 5) = 148
∴ 3x + (-20) = 148
∴ 3x - 20 = 148
→ Add 20 to both sides
∵ 3x - 20 + 20 = 148 + 20
∴ 3x = 168
→ Divide both sides by 3
∴ x = 56
→ To find m∠WZX, substitute x by 56 in its measure
∵ m∠WZX = 56 - 5
∴ m∠WZX = 51°
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Hope this helped :)