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2 years ago

How do you find x in this question?

Mathematics

1 answer:

ivanzaharov [21]2 years ago

7 0

Answer:

x = 70°

Step-by-step explanation:

The relevant relations are ...

base angles of an isosceles triangle are congruent
consecutive interior angles where parallel lines meet a transversal are supplementary

Triangle OBQ is isosceles, so angle OQB = 40°. Triangle OPQ is isosceles, so angle OQP is x. The sum of angles OQB and OQP is angle BQP, which is supplementary to angle OPQ. That is, ...

(40° +x) +x = 180°

2x = 140° . . . . . . subtract 40°

x = 70° . . . . . . divide by 2

_____

There are many ways to find x. The one shown here is just one of them. In general, right triangles, isosceles triangles, symmetry, inscribed angles can all be used to write relations involving the known angles and x.

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3 years ago

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