Answer :
Final answer:
To solve for m∠YXZ, one first expresses m∠WXY in terms of x and writes the equation for the measures of the angles. Solving this equation yields that x = 64. Subtracting m∠WXY from the total degrees in a right angle (90°), we find that m∠YXZ is 26°.
Explanation:
The subject of this question is Geometry, specifically the relationships between angles. Let's call m∠WXY = x. According to the problem, the measure of m∠WXV is eleven more than three times m∠WXY so we will call m∠WXV = 3x + 11. Since ∠WXZ is a right angle, it consists of two smaller angles, ∠WXY and ∠YXZ, so their measures add up to 90°. Therefore, m∠WXY + m∠YXZ = 90.
From the given information we also understand that m∠WXV is the exterior angle of the triangle, so its measure is equal to the sum of the measurements of the two non-adjacent angles in the triangle. That leads us to this equation: 3x + 11 = x + 139 or 2x = 128 which gives us x = 64.
To find m∠YXZ, we've already established that m∠WXY + m∠YXZ = 90, so substitute the value for ∠WXY: 64 + m∠YXZ = 90, and solve for m∠YXZ to get m∠YXZ = 26°.
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