6.1 Practice Assignment
Solve for x and find the measure of ZWZX? please help!

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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