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3 years ago

Please help w/ geometry!

Mathematics

1 answer:

lara [203]3 years ago

5 0

Answer:

<XYZ = 34

Step-by-step explanation:

Remark

Bisected angles means that the original angle (<XYZ in this case) has been cut exactly in half. The two parts that were created from <XYZ are equal so you need only solve for x, solve one of the halves and then double it.

Equation

3x - 7 = 2x + 1

Solution

3x - 7 = 2x + 1 Add 7 to both sides

3x - 7+7 = 2x +1+7 Combine

3x = 2x + 8 Subtract 2x

3x-2x = 2x-2x + 8 Collect like terms on both sides

x = 8

Solution 2

Find one of the bisected parts. You can choose either of the two parts so use 2x + 1

2x + 1

2*8+1

16 + 1

WYZ = 17 degrees

Solution 3

Double <WYZ to get <XYZ

<XYZ = 2 * 17

<XYZ = 34 degrees

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Read 2 more answers

Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Mice21 [21]

Answer:

$KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47$

Step-by-step explanation:

Given:

KL ║ NM ,

LM = 45

m∠M = 50°

KN ⊥ NM

NL ⊥ LM

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

$\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}$

Also

$m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}$ (angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

$NL=45\tan 50^{\circ}$

$m\angle KLN=m\angle LNM=40^{\circ}$ (alternate interior angles)

$m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ}$ (angles KNL and KLN are complementary).

So,

$\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08$

and

$\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47$