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bri9263
20.10.2019 •
Mathematics
Bailey got 7 bows for her birthday.at school,she lost a third of her bows.when she got home,she realized she had 42 bows left.how many bows did she have before her birthday? -
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Ответ:
Ответ:
In the circle, we can see that angle O and angle Q are both inscribed angles which intercepts an arc. Angle O intercepts arc RQP while angle Q intercepts arc ROP. The measure of each angle is measured to be one half of its intercepted arc, that is:
m ∠ O = m (arc PQR/2)
m ∠ Q = m (arc POR/2)
However we can also see that arcs RQP and ROP together make up the entire circle which has 360 degrees.
arc PQR + arc POR = 360°
therefore dividing both sides by 2:
arc PQR/2 + arc POR/2 = 180°
Then:
m ∠ O + m ∠ Q = m (arc PQR/2) + m (arc POR/2) = 180°
∠ O + ∠ Q = 180° are supplementary