Question

PLS HELP ME WITH THIS GEOMETRY QUESTION

Answer 1

Degree measure

m D = 66 degrees

m E = 97 degrees

m F = 17 degrees.

Answer is given below with explanations.

Explanation:

`given \: that \\ angle \: d \: = \: 4x - 2 \: degrees \\ angle \: e \: = 6x - 5 \: degrees \\ angle \: f \: = x \: degrees \\ in \: a \: triangle \: sum \: of \: three \: angles \: \\ of \: a \: triangle \: is \: 180 \: degrees. \\ then \: \\ angle \: d + \: \: angle \: e \ + \: angle \: f \: \: = 180 \\ (4x - 2) + (6x - 5) + x = 180 \\ 11x - 7 = 180 \\ adding \: 7 \: on \: both \: sides \\ 11x = 180 + 7 \\ 11x = 187 \\ x = (187)/(11) \\ x = 17 \\ angle \: d = 4x - 2 \\ \: \: = 4(17) - 2 \\ \: \: = 68 - 2 \: \\ \: \: angle \: d \: = 66 \: degrees \\ angle \: e \: = 6x - 5 \\ \: \: = 6(17) - 5 \\ \: \: = 102 - 5 \\ \: \: angle \: e=97 \: degrees \\ angl e \: f \: = x \\ then \: angle \: f \: = 17 \: degrees.`

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