Angles and Lines

Angles and Lines - Problem Solving


In parallelogram \(ABCD\), the green angle \(\angle ABC = 58 ^ \circ\). What is the pink angle \(\angle ADC\)?

In the above diagram, line segment \(\overline{AB}\) is parallel to line segment \(\overline{CD}.\) If \(\alpha={70}^\circ\) and \(\beta={28}^\circ,\) then what is the angle \(\angle OCD ?\)

Given quadrilateral \(ABCD\) where \(AB\) is parallel to \(DC\) and \(AC\) and \(BD\) intersect at \(E\), with \(\angle BEC = 58 ^\circ\) and \(\angle ACD = 31 ^\circ\), what is \(\angle ABE\) (in degrees)?

\(L_1\) is parallel to \(L_2\) and \(\alpha={54}^\circ,\) \(\beta={84}^\circ\) and \(\gamma={21}^\circ.\) What is the angle \(\omega\) in degrees?

Consider a 6 sided star that is formed from 2 triangles as above. What is the sum of the angles at A, B, C, D, E and F?


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