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ArbitrLikvidat [17]
3 years ago
9

Line ET is tangent to circle A at T, and the measure of Arc TG is 70°.

Mathematics
2 answers:
kow [346]3 years ago
8 0

<span>I will calculate this problem in two ways
</span>
alternative method 1
we know that
<span>The inscribed angle measures half of the arc it comprises.
</span>∠TNE=(1/2)*arc TG------> (1/2)*70°----> 35°

the triangle TEN is a right triangle
∠TNE+∠GET=90°-----> by complementary angles
∠GET=90-35---> 55°

the answer is
∠GET=55°

alternative method 2
we know that
<span>The measure of the external angle is the semi difference of the arcs that it covers.
</span>∠GET=(1/2)*[arc TN-arc TG]---> (1/2)*[180-70]---> (1/2)*110---> 55°

the answer is
∠GET=55°


ziro4ka [17]3 years ago
4 0
<span>Line ET is tangent to circle A at T
</span>
∴ ET ⊥ TN 
∴ ∠ ETN = 90
<span>the measure of Arc TG = 70
</span>
∠ TNG = half <span>the measure of Arc TG = 0.5 *70 = 35
</span>
<span>Δ ETN ⇒ The sum of all angles = 180
</span>
<span>∴∠ GET = ∠ NET = 180 - (90 + 35 ) = 55
</span>

∴ The correct answer is option <span>A. 55°</span>


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