Answer: x = 12
<u>Step-by-step explanation:</u>
a) Linear Pair: 110° + ∠a = 180° --> ∠a = 70°
b) congruent sides implies congruent angles --> ∠b = 70°
c) Triangle Sum Theorem: ∠a + ∠b + ∠c = 180
70° + 70° + ∠c = 180°
∠c = 40°
d) Complimentary Angles: ∠c + ∠d = 90°
40° + ∠d = 90°
∠d = 50°
∠2) Linear Pair: ∠d + ∠2 = 180°
50° + ∠2 = 180°
∠2 = 130°
x) m∠2 = 130°
10x + 10 = 130°
10x = 120
x = 12
93 x 2 = 186
x = 186 - 112
x = 74
y = 2(80) - 74
y = 160 -74
y = 86
360 - 112 - 74 - 86 = 88
z = (88+86)/2
z = 87
Answer:
1. x = 2
y = 1
2. x = 3 or 6 (Mistake or typo in problem)
3. y = 13
4. x = 7
y = 15
5. x = 4
Step-by-step explanation:
1. 6x - 3 = x + 7, 5x = 10, x = 2
3y + 2 = y + 4, 2y = 2, y = 1
2. There is most likely a typo. Either 8x = 24 and x = 3 or 2x + 10 = 3x + 4 and x = 6
3. 5y -3 = 2y + 36, 3y = 39, y = 13
4. 8y + 11 + 3y + 4 = 180, 11y + 15 = 180, 11y = 165, y = 15
7x = 3y + 4 = 49, x = 7
5. 7x - 10 = 4x + 2, 3x = 12, x = 4