Problem
GEO-B1-M08-P001 A Parallel Line and an Angle
#1
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), point \(D\) lies on \(AC\), and \(DE\parallel BC\), where \(E\) lies on \(AB\). If \(\angle A=46^\circ\), \(\angle B=71^\circ\), find \(\angle ADE\).
First find \(\angle C\), then use \(DE\parallel BC\).
In triangle \(ABC\), \(\angle C=180^\circ-46^\circ-71^\circ=63^\circ\). Since \(DE\parallel BC\), angle \(\angle ADE\) equals \(\angle ACB\). Therefore \(\angle ADE=63^\circ\).
A warm-up on choosing angle chasing after recognising parallelism.