Answer:
the second one
Step-by-step explanation:
Answer:
Step-by-step explanation:
How to factor expressions?
Find the G.C.F. and divide it into the terms of the expression you need to factor, like this:
. So I took the 12 and pulled it out of both terms, obtaining 
.
5. m∠C = 95°
6. m∠C = 70°
7. The other acute angle in the right triangle = 70°
8. m∠C = 70°
9. m∠C = 60° [equilateral triangle]
10. Measure of the exterior angle at ∠C = 110°
11. m∠B = 70°
12. m∠Z = 70°
<h3>What are Triangles?</h3>
A triangle is a 3-sided polygon with three sides and three angles. The sum of all its interior angles is 180 degrees. Some special triangles are:
- Isosceles triangle: has 2 equal base angles.
- Equilateral triangle: has three equal angles, each measuring 60 degrees.
- Right Triangle: Has one of its angles as 90 degrees, while the other two are acute angles.
5. m∠C = 180 - 50 - 35 [triangle sum theorem]
m∠C = 95°
6. m∠C = 180 - 25 - 85 [triangle sum theorem]
m∠C = 70°
7. The other acute angle in the right triangle = 180 - 90 - 25 [triangle sum theorem]
The other acute angle = 70°
8. m∠C = 180 - 55 - 55 [isosceles triangle]
m∠C = 70°
9. m∠C = 60° [equilateral triangle]
10. Measure of the exterior angle at ∠C = 50 + 60
Measure of the exterior angle at ∠C = 110°
11. m∠B = 115 - 45
m∠B = 70°
12. m∠Z = 180 - 35 - 75
m∠Z = 70°
Learn more about triangles on:
brainly.com/question/25215131
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Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π and cos A = cos B · cos C
scratchwork:
A + B + C = π
A = π - (B + C)
cos A = cos [π - (B + C)] Apply cos
= - cos (B + C) Simplify
= -(cos B · cos C - sin B · sin C) Sum Identity
= sin B · sin C - cos B · cos C Simplify
cos B · cos C = sin B · sin C - cos B · cos C Substitution
2cos B · cos C = sin B · sin C Addition
Division
2 = tan B · tan C
<u>Proof LHS → RHS</u>
Given: A + B + C = π
Subtraction: A = π - (B + C)
Apply tan: tan A = tan(π - (B + C))
Simplify: = - tan (B + C)
Substitution: = -(tan B + tan C)/(1 - 2)
Simplify: = -(tan B + tan C)/-1
= tan B + tan C
LHS = RHS: tan B + tan C = tan B + tan C 
