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Question
If ABC and DEF are similar triangles such that ∠A = 57° and ∠E = 73°, what is the measure of ∠C?
Solution
GIVEN: There are two similar triangles ΔABC and ΔDEF.
`∠A = 57^o ,∠ E = 73^o`
TO FIND: measure of `∠C`
SAS Similarity Criterion: If in two triangles, one pair of corresponding sides are proportional and the included angles are equal then two triangles are similar.
In ΔABC and ΔDEF if
`(AB)/(DE)=(AC)/(DE)`And
`∠ A=∠D`
Then, `ΔABC∼ Δ DEF`
So,
`∠ A=∠D`
`∠D= 57^o`
Now we know that sum of all angles of a triangle is equal to 180°,
`∠A + ∠B+∠ C= 180^o `
`57^o +73^o +∠C= 180^o`
`130^o+∠C =180^o`
`∠C= 50^o`
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