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2 years ago

I need help, this is geometry

Mathematics

2 answers:

mamaluj [8]2 years ago

8 0

Answer:

∠R = 21°

∠Q = 120°

∠P = 39°

Step-by-step explanation:

Step 1:

6x - 6° + 2x - 3° + x = 180° Sum of a Δ

Step 2:

9x - 9° = 180° Combine Like Terms

Step 3:

9x = 189° Add 9 on both sides

Step 4:

x = 189° ÷ 9 Divide

Step 5:

x = 21°

Step 6:

2 ( 21 ) - 3 = ∠P = 39°

Step 7:

6 ( 21 ) - 6 = ∠Q = 126°

Step 8:

∠R = 21°

Answer:

∠R = 21°

∠Q = 120°

∠P = 39°

Hope This Helps :)

Artemon [7]2 years ago

7 0

Answer:

∠P = 39º

∠Q=120º

∠R = 21º

Step-by-step explanation:

m∠P+m∠Q+m∠R=180º (sum of ∠s in a triangle)

2x-3+6x-6+x=180º (substitution)

9x-9=180º (algebra)

9x=189º (algebra)

x=21º (algebra) (this is ∠R)

(2x-3)=39º (algebra) (this is ∠P)

6x-6=120º (algebra) (this is ∠Q)

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Answer:

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Step-by-step explanation:

Given:

KL ║ NM ,

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

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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).

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