QuestionAugust 10, 2025

If overline (CF) is an altitude of Delta CDE find mangle CEF if mangle CFE=(3x+36)^circ and mangle FCE=(2x+18)^circ A. 18^circ B. 36^circ C. 54^circ D. 90^circ

If overline (CF) is an altitude of Delta CDE find mangle CEF if mangle CFE=(3x+36)^circ and mangle FCE=(2x+18)^circ A. 18^circ B. 36^circ C. 54^circ D. 90^circ
If overline (CF) is an altitude of Delta CDE find mangle CEF if mangle CFE=(3x+36)^circ and mangle FCE=(2x+18)^circ A. 18^circ B. 36^circ C. 54^circ D. 90^circ

Solution
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Answer

D. 90^{\circ } Explanation 1. Identify the relationship Since \overline{CF} is an altitude, \angle CFE + \angle FCE = 90^\circ. 2. Set up the equation (3x + 36)^\circ + (2x + 18)^\circ = 90^\circ 3. Solve for x Combine terms: 5x + 54 = 90. Solve: 5x = 36, so x = 7.2. 4. Calculate m\angle CEF Substitute x: m\angle CFE = (3x + 36)^\circ = (3 \times 7.2 + 36)^\circ = 57.6^\circ. m\angle FCE = (2x + 18)^\circ = (2 \times 7.2 + 18)^\circ = 32.4^\circ. \angle CEF = 180^\circ - (\angle CFE + \angle FCE) = 180^\circ - 90^\circ = 90^\circ.

Explanation

1. Identify the relationship<br /> Since $\overline{CF}$ is an altitude, $\angle CFE + \angle FCE = 90^\circ$.<br />2. Set up the equation<br /> $(3x + 36)^\circ + (2x + 18)^\circ = 90^\circ$<br />3. Solve for $x$<br /> Combine terms: $5x + 54 = 90$. Solve: $5x = 36$, so $x = 7.2$.<br />4. Calculate $m\angle CEF$<br /> Substitute $x$: $m\angle CFE = (3x + 36)^\circ = (3 \times 7.2 + 36)^\circ = 57.6^\circ$.<br /> $m\angle FCE = (2x + 18)^\circ = (2 \times 7.2 + 18)^\circ = 32.4^\circ$.<br /> $\angle CEF = 180^\circ - (\angle CFE + \angle FCE) = 180^\circ - 90^\circ = 90^\circ$.
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