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°.
There is no solution because the two lines don't intersect.
Answer:
96 square inches
Step-by-step explanation:
The scale is 2 inches : 3 feet
Thus for 18 feet in Serika's real house, the model is 18 * (2"/3') = 12 inches
For 12 feet in Serika's real house, the model is 12 * (2"/3') = 8 inches
Area of carpeting needed in Serika's dollhouse = 12" * 8" = 96 square inches
Answer:
infinite solutions
Step-by-step explanation:
Multiply the first equation by 2
2(3x-5y) = 2*15
6x - 10y = 30
This is the same as the second equation
They are the same line
This means there are infinite solutions
