The transitive property of angle congruence states that if ________ ≅ ∠QRS and ∠QRS ≅ ∠PQR, then ∠XYZ ≅ ∠PQR . A) ∠XQR B) ∠QRS C
2 answers:
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The value of x is 27°.
Solution:
Given .
∠A = 3x – 10, ∠C = 45°, ∠D = 2x + 10
<em>If two triangles are congruent, then the angles are congruent.</em>
∠A = ∠E (Alternate interior angles)
∠C = ∠C (Reflexive property)
∠B = ∠D (Alternative interior angles)
⇒ ∠B = 2x + 10
<em>Sum of the interior angles of the triangle = 180°</em>
In ΔACB,
3x – 10 + 45° + 2x + 10 = 180°
5x + 45° = 180°
Subtract 45° on both sides of the equation.
5x = 135°
Divide by 5 on both sides of the equation.
x = 27°
The value of x is 27°.
Using proportions, it is found that:
- Peter is walking at a rate of 3 km/h.
- MJ is biking at a rate of 9 km/h.
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- Peter is walking at a rate of x km/h.
- MJ is biking 6 km/h faster than Peter, thus 6 + x km/h.
- Opposite directions, thus, their distance increases at a rate of (6 + 2x) km each hour, as
.
6 + 2x km each hour, 18 km after 1.5 hours, thus, the rule of three is:
1h - (6 + 2x) km
1.5h - 18 km
Applying cross multiplication:
Then:
- Peter is walking at a rate of 3 km/h.
- MJ is biking at a rate of 9 km/h.
A similar problem is given at brainly.com/question/24112433