Where is the math u are talking about
Nothing else is given, so for the two triangles to be congruent, the only possible proof is the ASA theorem.
first pairs of angles: 2x+7=x+21 => x=14
second pairs of angles: 8y-4=4y+28 =>y=8
The two triangles share the same side PR
Based on the Angle-Side-Angle Triangle Congruence theorem, these two triangles are congruent with x=14, y=8
(2x+7) +(8y-4) +Q=180 =>85
Sin θ = opposite leg/hypotenuse
csc θ = hypotenuse /opposite leg =8/7
cot <span>θ = adjacent leg/opposite leg
hypotenuse =8
opposite leg =7
We need to find adjacent leg.
(Opposite leg)² +(adjacent leg)² = hypotenuse²
7² + </span>(adjacent leg)² =8²
(adjacent leg)² = 64 - 49
(adjacent leg)² = 15
adjacent leg=+/-√15
<span>WE need only positive root,
so </span>adjacent leg =√15
cot θ = √15/7 or 0.5533<span>
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