Geo: Worth 50 points and I will give brainliest to right answer! #24

Mathematics

1 answer:

Sindrei [870]2 years ago

6 0

1. ∠1 ≅ ∠3 1. given

∠1 and ∠6 are supplementary angles

∠3, ∠4, and ∠5 are supplementary angles

2. m∠1 = m∠3 2. definition of congruency

3. m∠1 + m∠6 = 180° 3. definition of supplementary angles

m∠3 + m∠4 + m∠5 = 180°

4. m∠3 + m∠4 + m∠5 = m∠1 + m∠6 4. transitive property

5. m∠3 + m∠4 + m∠5 = m∠3 + m∠6 5. substitution property

6. m∠4 + m∠5 = m∠6 6. subtraction property of equality

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Help again...its for math offering 15 points

Anettt [7]

Answer:

$\tan \dfrac{\theta}2 = \dfrac{1}2$

Step by step Explanation:

$\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right]$

$=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2$