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3 years ago

Circles and angles/arcs could someone help me with this geometry question please?

Mathematics

1 answer:

Elden [556K]3 years ago

3 0

9514 1404 393

Answer:

arc AB = 60°
arc BC = 78°
arc EF = 40°
angle AFB = 30°

Step-by-step explanation:

The relevant relations are ...

the measures of an arc and its central angle are the same
the sum of the arcs of a circle is 360°
the measure of an inscribed angle is half the measure of the arc it intercepts

Arc AB has the measure of central angle AOB, 60°.

Arc EF has double the measure of inscribed angle EAF, so is 40°.

Arc BC completes the circle, so has measure ...

arc BC = 360° -arc FA -arc AB -arc CE -arc EF

arc BC = 360° -140° -60° -42° -40°

arc BC = 78°

Angle AFB is half the measure of arc AB, so is 60°/2 = 30°.

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3 years ago

The sides of a triangle have lengths of x, x + 5, and 25. If the longest side is 25, which of the following values of x would ma

Amiraneli [1.4K]

In a right angle, the sum of the squares of the two shorter sides is equal to the square of the longest side.
Here, the longest side is 25, the shorter sides are x and x+5.

$x^2+(x+5)^2=25^2 \\
x^2+x^2+10x+25=625 \\
2x^2+10x+25=625 \ \ \ |-625 \\
2x^2+10x-600=0 \ \ \ |\div 2 \\
x^2+5x-300=0 \\
x^2+20x-15x-300=0 \\
x(x+20)-15(x+20)=0 \\
(x-15)(x+20)=0 \\
x-15=0 \ \lor \ x+20=0 \\
x=15 \ \lor \ x=-20
$

The length of a side must be a positive number, so x=15.
The answer is C.

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4 years ago