What is the measure of spq in the figure below
Asked by maham237 @ in Mathematics viewed by 253 People
Answered by maham237 @
Notice the PS and PQ sides, both are 10 in length.
now notice the PR side, is shared by both triangles, so is the same length for both.
the only way QR have a right-angle and hit R, at the same exact place SR hits R and yet also with a right angle, is that SR and QR are both the same length.
so, if all those lengths are the same length in each triangle, the triangles are congruent by SSS, that means the ray PR is an angle bisector, so is splitting that angle into two equal halves. We know one of the halves is 28°, therefore the other half must be the same, since its her twin.
therefore ∡SPQ is the sum of those twins.
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