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2 answers:
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so in short, the only factoring doable to it, without any complex factors, is that of taking the common factor of 2x.
now, the trinomial of 2x²+x+1, will not give us any "real roots", just complex or "imaginary" ones.
if you have already covered the quadratic formula, you could test with that, or you can also check that trinomial's discriminant, and notice that it will give you a negative value.
Answer:
see below
Step-by-step explanation:
There are a few relevant relations involved:
- an inscribed angle is half the measure of the arc it intercepts
- an arc has the same measure as the central angle that intercepts it
- the angle exterior to a circle where secants meet is half the difference of the intercepted arcs (near and far)
- the angle interior to a circle where secants meet is half the sum of the intercepted arcs
- the angle where tangents meet is the supplement of the (near) arc intercepted
- an exterior angle of a triangle is equal to the sum of the remote interior angles
- the angle between a tangent and a radius is 90°
- the angle sum theorem
AB is a diameter, so arcs AB are 180°.
a) BC is the supplement to arc AC: 180° -140° = 40°
b) BG is the supplement to AG: 180° -64° -38° = 78°
c) ∠1 has the measure of BC: 40°
d) ∠2 is inscribed in a semicircle, so has measure 180°/2 = 90°
e) ∠3 is half the measure of arc AE: 64°/2 = 32°
f) ∠4 is half the sum of arcs AG and BC: ((64°+38°) +40°)/2 = 71°
g) ∠5 is half the difference of arcs AC and EG: (140° -38°)/2 = 51°
h) ∠6 is half the sum of arcs EAC and BG: ((140°+64°) +78°)/2 = 141°
i) ∠7 is the difference of exterior angle 4 and interior angle 1: 71° -40° = 31°
j) ∠8 is the measure of arc AC: 140°
k) ∠9 is the supplement to arc AC: 180° -140° = 40°
l) ∠10 is the complement of angle 7: 90° -31° = 59°
