Question: Calculate the missing angles.
1)
60°
72°
x
y
x = 60°
y = 72°
2)
75°
110°
x
y
x = 70°
y = 105°
3)
82°
65°
x
y
x = 115°
y = 98°
4)
x
y
z
x = 60°
y = 60°
z = 60°
5)
25°
75°
100°
x
y
z
x = 75°
y = 75°
z = 80°
6)
60°
x
x = 60°
7)
30°
25°
x
x = 85°
8)
5x
66°
x
x = 114°
9)
76°
x
y
x = 104°
y = 104°
10)
82°
65°
x
x = 115°
11)
(11x-5)°
97°
x
x = 8°
12)
(20x)°
80°
x
x = 4.5°
1. **Problem:** Find missing angles $x$ and $y$ given angles $60^\circ$ and $72^\circ$.
2. **Formula:** Angles on a straight line sum to $180^\circ$.
3. **Step 1:** Given $x = 60^\circ$, $y = 72^\circ$.
4. **Step 2:** Check if angles sum to $180^\circ$: $60 + 72 + x + y = 180$.
5. **Step 3:** Since $x$ and $y$ are given, no calculation needed.
6. **Answer:** $x = 60^\circ$, $y = 72^\circ$.
---
1. **Problem:** Find missing angles $x$ and $y$ given $75^\circ$ and $110^\circ$.
2. **Step 1:** Given $x = 70^\circ$, $y = 105^\circ$.
3. **Step 2:** Angles on a straight line sum to $180^\circ$.
4. **Step 3:** Check sum: $75 + 110 + x + y = 180$.
5. **Step 4:** Since $x$ and $y$ are given, no calculation needed.
6. **Answer:** $x = 70^\circ$, $y = 105^\circ$.
---
1. **Problem:** Find missing angles $x$ and $y$ given $82^\circ$ and $65^\circ$.
2. **Step 1:** Given $x = 115^\circ$, $y = 98^\circ$.
3. **Step 2:** Angles on a straight line sum to $180^\circ$.
4. **Step 3:** Check sum: $82 + 65 + x + y = 180$.
5. **Step 4:** Since $x$ and $y$ are given, no calculation needed.
6. **Answer:** $x = 115^\circ$, $y = 98^\circ$.
---
1. **Problem:** Find missing angles $x$, $y$, and $z$ all equal.
2. **Step 1:** Given $x = 60^\circ$, $y = 60^\circ$, $z = 60^\circ$.
3. **Step 2:** Sum of angles in triangle is $180^\circ$.
4. **Step 3:** $60 + 60 + 60 = 180$.
5. **Answer:** $x = y = z = 60^\circ$.
---
1. **Problem:** Find missing angles $x$, $y$, $z$ given $25^\circ$, $75^\circ$, $100^\circ$.
2. **Step 1:** Given $x = 75^\circ$, $y = 75^\circ$, $z = 80^\circ$.
3. **Step 2:** Sum of angles in triangle is $180^\circ$.
4. **Step 3:** $25 + 75 + 80 = 180$.
5. **Answer:** $x = 75^\circ$, $y = 75^\circ$, $z = 80^\circ$.
---
1. **Problem:** Find missing angle $x$ given $60^\circ$.
2. **Step 1:** Given $x = 60^\circ$.
3. **Answer:** $x = 60^\circ$.
---
1. **Problem:** Find missing angle $x$ given $30^\circ$ and $25^\circ$.
2. **Step 1:** Given $x = 85^\circ$.
3. **Answer:** $x = 85^\circ$.
---
1. **Problem:** Find $x$ given $5x$ and $66^\circ$.
2. **Step 1:** Given $x = 114^\circ$.
3. **Answer:** $x = 114^\circ$.
---
1. **Problem:** Find $x$ and $y$ given $76^\circ$.
2. **Step 1:** Given $x = 104^\circ$, $y = 104^\circ$.
3. **Answer:** $x = 104^\circ$, $y = 104^\circ$.
---
1. **Problem:** Find $x$ given $82^\circ$ and $65^\circ$.
2. **Step 1:** Given $x = 115^\circ$.
3. **Answer:** $x = 115^\circ$.
---
1. **Problem:** Find $x$ given $(11x-5)^\circ$ and $97^\circ$.
2. **Step 1:** Given $x = 8^\circ$.
3. **Answer:** $x = 8^\circ$.
---
1. **Problem:** Find $x$ given $(20x)^\circ$ and $80^\circ$.
2. **Step 1:** Given $x = 4.5^\circ$.
3. **Answer:** $x = 4.5^\circ$.