What is the length of ML
1 answer:
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Given:
The figure of a quadrilateral ABCD.
To find:
The perimeter of the quadrilateral ABCD.
Solution:
In an isosceles triangle, the two sides and base angles are congruent.
In triangle ABD,
[Given]
is an isosceles triangle [Base angle property]
[By definition of isosceles triangles]
...(i)
In triangle BCD,
[Given]
All interior angles of the triangle BCD are congruent, so the triangle BCD is an equilateral triangle and all sides of the triangle area equal.
[Using (i)] ...(ii)
Now, the perimeter of quadrilateral ABCD is:
Therefore, the perimeter of the quadrilateral ABCD is 35 units.
Answer: see proof below
<u>Step-by-step explanation:</u>
Given: cos 330 =
Use the Double-Angle Identity: cos 2A = 2 cos² A - 1
Proof LHS → RHS:
LHS cos 165
Double-Angle: cos (2 · 165) = 2 cos² 165 - 1
⇒ cos 330 = 2 cos² 165 - 1
⇒ 2 cos² 165 = cos 330 + 1
Given:
Divide by 2:
Square root:
Scratchwork:
Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE
LHS = RHS
