In cyclic quadrilateral PQRS
∠P3=∠Q4=∠R5
Find the largest angle in quadrilateral in degrees.
+118716 Opposite angles in a cyclic quad are suplementar
Givew those equalities I can see that
The smallest would add with the biggest to get 180 degrees
The largest angle could be
∠q4=∠r5∠q=0.8∗∠r ∠q+∠r=180∘0.8∗∠r+∠r=180∘1.8∗∠r=180∘∠r=100∘∠q=80∘ ∠p3=∠r5∠p3=1005∠p=60∘so∠s=120∘
LaTex:
\frac{\angle q}{4}=\frac{\angle r}{5}\\
\angle q=0.8*\angle r\\~\\
\angle q + \angle r =180^ \circ\\
0.8*\angle r + \angle r =180^ \circ\\
1.8*\angle r =180^ \circ\\
\angle r =100^ \circ\\
\angle q = 80 ^\circ\\~\\
\frac{\angle p}{3}=\frac{\angle r}{5}\\
\frac{\angle p}{3}=\frac{100}{5}\\
\angle p = 60^\circ\\
so\\
\angle s = 120 ^\circ
