Answer:
74°
Step-by-step explanation:
A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.
According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.
The remaining angle of the rhombus will be calculated as thus;
= 360° - (32°+32°)
= 360° - 64°
= 296°
This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°
This means that each obtuse angles of the rhombus will be 148°.
To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.
m° = 148°/2
m° = 74°
Hence the angle measure if m(1) is 74°
Answer:
the answer is 0 because it 3 negative number
(x + 2)(x - 4)
= x^2 + 2x - 4x - 8
= x^2 - 2x - 8
Answer:
Height of the goalpost is 9.25 m.
Step-by-step explanation:
As per the rule of reflection in physics,
Angle of incidence = Angle of reflection
As we can see in the picture attached, both the angles (θ) are equal.
m∠ACB = m∠ECD = 90° - θ
m∠ABC = m∠ADC = 90°
Therefore, both the triangles ΔABC and ΔEDC will be similar.
And by the property of similar triangles, their corresponding sides will be proportional.


ED = 
ED = 9.25 m
Height of the goalpost is 9.25 m.
Answer: Yes the ladder will reach the fire
Step-by-step explanation: Please refer to the attached diagram for details.
The fire is at point A, while the top of the truck is at point C. The fire is actually burning at 22 feet off the ground, but because the fire truck itself is already 6 feet off the ground, the point that would serve as the base of the building would be 16 feet from the third floor (which is 22 feet minus 6 feet). Hence, point A to point B is 16 feet. So we need to calculate if line AC (from the truck to the fire at the third floor, labeled as b) shall equal the length of the ladder which is 16-foot long.
The angle of the ladder with the top of the truck is 75 degrees. Therefore,
Sin 75 = opposite/hypotenuse
Sin 75 = 16/b
By cross multiplication we now have
b = 16/Sin 75
b = 16/0.9659
b = 16.56
If the distance from A to C is 16.56 feet, then the 16-foot long ladder would reach the fire.