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4 years ago

If Lines M and L are parallel, and angle 1 is 110 degrees, what are the measures of all 7 other angles.

Mathematics

2 answers:

Artemon [7]4 years ago

8 0

Angle 1 = 110
Angle 2 = 70
Angle 3 = 110
Angle 4 = 70
Angle 5 = 70
Angle 6 = 110
Angle 7 = 70
Angle 8 = 110

LiRa [457]4 years ago

3 0

Solution:

we are given with a diagram in which we have

Lines M and L are parallel, and angle 1 is 110 degrees.

we have been asked to find the measures of all 7 other angles.

as we know when a straight line intersect a pair of parallel lines then their corresponding and alternate angles are equal so

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3 years ago

The length of triangle base is 26. A line, which is parallel to the base divides the triangle into two equal area parts. Find th

Yanka [14]

Answer:

Step-by-step explanation:

It is given that the length of triangle base is 26, then let ABC be the triangle and BC be the base of the triangle=26.Let DE be the parallel line to the base that divides triangle ABC into two equal area parts.

Now, Let AD=a, DB=b, DE=c, AE=d and EC=e, then

Since, triangle ABC is similar to triangle ADE, thus using basic proportions, we get

$\frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}$

$\frac{AD}{AD+DB}=\frac{DE}{BC}=\frac{AE}{AE+EC}$

$\frac{a}{a+b}=\frac{c}{26}=\frac{d}{d+e}$

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$c=\frac{26a}{a+b}$

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4 years ago

Is anyone good at geometry if so can you help me please ?

Pachacha [2.7K]

The arcs FA, AB, and <u>BF</u> make up the entire circle, so their measures sum to 360°:

arcFA + arcAB + arcBF = 360° → arcBF = 360° - 160° - 140° = 60°

By the inscribed angle theorem, angle BAF has measure equal to half of that of arc BF, so

angleBAF = 30°

By the secant-tangent theorem (not sure if there's an official name for it), the measure of angle ACF is equal to half the difference of the arcs it intercepts, namely BF and FA, so that

angleACF = 1/2 (arcFA - arcBF) = 1/2 (160° - 60°) = 50°

Now use the law of sines for solve for FA:

sin(angleACF) / FA = sin(angleBAF) / FC

sin(50°) / FA = sin(30°) / 10

FA = 10 sin(50°) / sin(30°) ≈ 15.3

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