x = 4 and EF = 4 ⇒ 3rd answer
Step-by-step explanation:
If two triangles are congruent, then
1. Their corresponding sides are equal
2. Their corresponding angles are equal
3. Their areas and perimeters are equal
∵ △ ABC ≅ △ DEF
∴ AB ≅ DE
∴ BC ≅ EF
∴ AC ≅ DF
∵ BC = 4 x - 12
∵ EF = -3 x + 16
∵ BC = EF
∴ 4 x - 12 = -3 x + 16
Let us solve the equation to find x
∵ 4 x - 12 = -3 x + 16
- Add 3 x for both sides
∴ 7 x - 12 = 16
- Add 12 to both sides
∴ 7 x = 28
- Divide both sides by 7
∴ x = 4
Substitute the value of x in the expression of EF
∵ EF = -3 x + 16
∵ x = 4
∴ EF = -3(4) + 16 = -12 + 16
∴ EF = 4
x = 4 and EF = 4
Learn more:
You can learn more about congruence of Δs in brainly.com/question/3202836
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The vertical angles are equal to each other, that is, one of the one-sided corners will be 116°.
The sum of the one-sided angles is 180°, which means: 4x+116 = 180°
4x = 180-116 => 4x = 64°
x = 64/4 = 16°.
The sum of two adjacent angles is 180°. which means, that: 2x-3y = 180-64 = 116°
2x-3y = 116°
-2x+3y = -116
-32+3y = -116
3y = -116-(-32)
3y = -84
y = -84/3 => y = -28.
