1. segment HE + segment PE = segment HP
9x + x + 4 = n
We must add the like terms.
10x + 4 = n
n = 10x + 4
So, it will take 10x + 4 steps to point P from point H.
2. segment HE + segment PE = segment HP
3x + 2 + 5x = n
Add the like terms.
7x + 2 = n
n = 7x + 2
Therefore, it will take you 7x + 2 steps from point H to walk to point P.
3. Measure of angle HOP = 60°
Solution:
Earlier, it was mentioned that the triangles HOE and POE are right triangles and formed right angles.
Also, the sum of the interior angles of a triangle is 180.
Angle H + Angle O + Angle E = 180°
Angle H + 30° + 90° = 180°
Angle H + 120° = 180°
Angle H = 180° - 120°
Angle H = 60°
4.
Angle P + Angle POE + Angle E = 180°
x + 2x - 30 + 90° = 180°
3x° + 60° = 180°
3x° = 180° - 60°
3x = 120°
x = 40°
The value of x is 40°.
5. Angle HOE + Angle OHE + Angle HEO = 180°
x + 2x + 90° = 180°
Add like terms.
3x + 90° = 180°
3x = 180° - 90°
3x = 90°
x = 30°
The value of x is 30. Let's go back to our angles.
Angle HOE = x = 30°
Angle OHE = 2x = 2(30°) = 60°
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Answers & Comments
Answer:
1. segment HE + segment PE = segment HP
9x + x + 4 = n
We must add the like terms.
10x + 4 = n
n = 10x + 4
So, it will take 10x + 4 steps to point P from point H.
2. segment HE + segment PE = segment HP
3x + 2 + 5x = n
Add the like terms.
7x + 2 = n
n = 7x + 2
Therefore, it will take you 7x + 2 steps from point H to walk to point P.
3. Measure of angle HOP = 60°
Solution:
Earlier, it was mentioned that the triangles HOE and POE are right triangles and formed right angles.
Also, the sum of the interior angles of a triangle is 180.
Angle H + Angle O + Angle E = 180°
Angle H + 30° + 90° = 180°
Angle H + 120° = 180°
Angle H = 180° - 120°
Angle H = 60°
4.
Solution:
Angle P + Angle POE + Angle E = 180°
x + 2x - 30 + 90° = 180°
Add the like terms.
3x° + 60° = 180°
3x° = 180° - 60°
3x = 120°
x = 40°
The value of x is 40°.
5. Angle HOE + Angle OHE + Angle HEO = 180°
x + 2x + 90° = 180°
Add like terms.
3x + 90° = 180°
3x = 180° - 90°
3x = 90°
x = 30°
The value of x is 30. Let's go back to our angles.
Angle HOE = x = 30°
Angle OHE = 2x = 2(30°) = 60°