Question

The diagram shows FGCE is the image of ABCD under and isometry. Given BCG is a straight line, determine angle DCE

A. 36°
B. 67°
C. 54°
D. 46°​

Answer 1

D

Explanation:

The sum of the interior angles of a quadrilateral = 360°

∠ BCD = 360° - (90 + 90 + 113)° = 360° - 293° = 67°

ABCD and FGCE are congruent figures , then

∠ GCE = ∠ BCD = 67°

BCG isa straight line , so

∠ BCD + ∠DCE + ∠ GCE = 180° , that is

67° + ∠ DCE + 67° = 180°

∠ DCE + 134° = 180° ( subtract 134° from both sides )

∠ DCE = 46° → D