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Find m∠BOC, if m∠MOP = 110°.
Answer:
m∠BOC= 40 degrees
Step-by-step explanation:
A diagram has been drawn and attached below.
- OM bisects AOB into angles x and x respectively
- ON bisects ∠BOC into angles y and y respectively
- OP bisects ∠COD into angles z and z respectively.
Since ∠AOD is a straight line
x+x+y+y+z+z=180 degrees
We are given that:
m∠MOP = 110°.
From the diagram
∠MOP=x+2y+z
Therefore:
x+2y+z=110°.
Solving simultaneously by subtraction
x+2y+z=110°.
We obtain:
x+z=70°
Since we are required to find ∠BOC
∠BOC=2y
Therefore from x+2y+z=110° (since x+z=70°)
70+2y=110
2y=110-70
2y=40
Therefore:
m∠BOC= 40 degrees
Answer:2. Given the points A, B, C, D, calculate:
(a) the angle B of the triangle ABC
(b) the area of the triangle ABC
(c) the median BE of the triangle ABC
(d) the height AH of the triangle ABC
(e) the volume of tetrahedron ABCD
(f) the point E so that ABCE is a parallelogram.
A(-1, 2, -3), B(4, -1, 0), C(2, 1, -2), D( 3,4,5)
Step-by-step explanation:
