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stepladder [879]
3 years ago
7

Given: circle: k(O), m∠A = 101° m∠L = 79°, m LK = 122° Find: m AJ

Mathematics
1 answer:
AlekseyPX3 years ago
3 0

Answer:

∠ J = 58°

Step-by-step explanation:

Given:

∠ A = 101°

∠ L = 79°

∠ K = 122°

Find:

∠ J = ?

Computation:

We know that, Sum of all angle in a circle is 360°

So,

⇒ ∠ A + ∠ L + ∠ K + ∠ J = 360°

⇒ 101°  + 79°  + 122°  +  ∠ J = 360°

⇒ 302°  +  ∠ J = 360°

⇒ ∠ J = 360° - 302°

∠ J = 58°

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3 years ago
Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.
Vikentia [17]

The relationship between Traingle XYZ and ACB is that they are similar triangles. tanX = tanA = 5 over 2 and 5 tenths, where

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  • CB = 2 x  YZ

<h3>What is the dilation about?</h3>

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, hence XYZ and ACB are similar triangles.

Angles Y and C are said to measure 90 degrees, and angles A and X are known to be congruent. Thus:

tanX = tanA = 5 over 2 and 5 tenths

AC = 2 x  XY

CB = 2 x  YZ

Another way to solve for it is by:

Note that Dilation of the triangle ΔXYZ was by a factor of "2".

Since m∠Y = m∠C = 90º   - given

ΔXYZ and ΔACB are said to be right triangles.

Since ∠X ≅ ∠A   - given

Then ∠X and ∠Z are  said to becomplementary angles

Since m∠Z = 90° - m∠X   -- given

Then ∠A and ∠B are said to be complementary angles

Since m∠B = 90° - m∠A  --- given

Then, ∠Z ≅ ∠B

Therefore ΔXYZ ∼ ΔACB are  similar triangles because it has its corresponding sides to be proportional and its corresponding angles to be congruent.

Note:

sin ∠X = 5/5.59

sin ∠X = YZ/XY

YZ = 5  seen in ΔXYZ

XZ = 5.59 seen in hypotenuse of ΔXYZ

Then one need to Calculate the length of one aspect of XY:

XY = √((5.59)2 - 52)

= 2.4996

Note CB/YZ = 2

CD = 2*YZ = 2 x 5

= 10

AC/XY = 2

AC = 2* XY

= 2 x 2.4996

= 4.999

Learn more about dilation from:

brainly.com/question/27517432

#SPJ1

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2 years ago
To determine how a city’s residents feel about building a new youth center, a group considers surveying 50 random children at a
Lemur [1.5K]
This would result in a biased sample because:

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most of those kids are more likely than not to want a youth center, so most of them will naturally agree without a doubt for the need of a youth center

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- in final words the reason why this survey will be biased is because there is no variety in the participants being tested. It is basically just asking teachers she students their preference, excluding the rest of an entire community

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