The value of x as evident in the task content is; 14 and hence, the measure of angles m<DEC and m< CEF are; 142° and 38° respectively.
What are the justification s for the statements as indicated in the task content?
It follows from the task content that the justifications of the statements are to be indicated.
On this note, the justifications are as follows;
- m<DEF = 180°; The measure of angle on a line is 180°.
- m<DEC + m<CEF = 180; The algebraic sum of angles on a straight line is; 180°.
- (11x -12) + (2x +10) = 180; Substitute the given expressions for the angles DEC and CEF respectively.
- 13x - 2 = 180; Collect like terms.
- 13x = 182; Add 2 to both sides of the equation.
- x = 14; Divide both sides of the equation by 13.
Hence, the measure of angle; m<DEC = 11x -12.
= 11(14) - 12
= 142°.
Ultimately, the measure of angle m<CEF is;
m<CEF = 180 -142
m<CEF = 38°.
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