Answer:
x = 17
Step-by-step explanation:
Since the triangles are congruent, the angles are equal
I≅ P
3x+4 = 72-x
Add x to each side
3x+4+x = 72-x+x
4x+4 = 72
Subtract 4 from each side
4x+4-4 = 72-4
4x= 68
Divide by 4
4x/4 = 68/4
x = 17
Answer:
17.8 meters
Step-by-step explanation:
Given:
before expansion railroad rail= 4 km
expansion= 16 cm
railroad makes an isosceles triangle at the center of the rail when it expands
The base of the triangle=4 km
As 1km=100,000 cm
thus 16 cm= 16/100,000 km
each side of this triangle= (4 + 16/100,000) / 2 = 4.0001 / 2 = 2.00008 km
One half of the isosceles triangle makes a right triangle with one of the side =4 / 2 = 2 km
and the hypotenuse = 2.00008 km
Using Pythagoras theorem to find the third side of this right angles triangle:
c^2=a^2+b^2
2.00008^2= 2^2 + b^2
2.00008^2 - 2^2=b^2
b=0.0178 km
b= 17.8 m
hence, approximately 17.8 meters would the center of the rail rise above the ground!
Answer:
The measure of Angle G is 62.5°.
Step-by-step explanation:
Given:
Δ EFG is an Isosceles Triangle.
EG = EF
m∠ E = 55°
To Find:
m∠ G = ?
Solution:
Δ EFG is an Isosceles Triangle. ........Given
EG = EF ..............Given
∠ G = ∠ F = x (say) ..................Isosceles triangle property
Now in Δ EFG we have
∠ E + ∠ G + ∠ F = 180° .......... Angle sum property of triangle
On substituting the values we get
The measure of Angle G is 62.5°.
Answer:
6) x = 36°, y = 18°
7) z = 7°
Step-by-step explanation:
6) 2x + 3x = 180°
5x = 180°
x = 36°
4y = 2x = 72°
y = 18°
7) 2z + 4 = 4z - 10
2z = 14
z = 7
