Angle Calculations 63D239

1. Problem: Find the unknown angle $x$ when two adjacent angles on a straight line are $46^\circ$ and $x$. 2. Formula: Adjacent angles on a straight line sum to $180^\circ$. 3. Work: $$46^\circ + x = 180^\circ$$ $$x = 180^\circ - 46^\circ$$ $$x = 134^\circ$$ 4. Explanation: Since the two angles form a straight line, their sum must be $180^\circ$. Subtracting $46^\circ$ from $180^\circ$ gives the value of $x$. --- 1. Problem: Find the unknown angle $x$ when two adjacent angles are $133^\circ$ and $x$. 2. Formula: Adjacent angles on a straight line sum to $180^\circ$. 3. Work: $$133^\circ + x = 180^\circ$$ $$x = 180^\circ - 133^\circ$$ $$x = 47^\circ$$ 4. Explanation: The two angles are adjacent on a straight line, so their sum is $180^\circ$. Subtracting $133^\circ$ from $180^\circ$ gives $x$. --- 1. Problem: Find the unknown angle $x$ when a right angle is split by a diagonal ray into two angles $21^\circ$ and $x$. 2. Formula: The sum of angles in a right angle is $90^\circ$. 3. Work: $$21^\circ + x = 90^\circ$$ $$x = 90^\circ - 21^\circ$$ $$x = 69^\circ$$ 4. Explanation: The diagonal ray splits the right angle into two parts. Subtracting $21^\circ$ from $90^\circ$ gives $x$. --- 1. Problem: Find the unknown angle $x$ when two adjacent angles are $66^\circ$ and $x$. 2. Formula: Adjacent angles on a straight line sum to $180^\circ$. 3. Work: $$66^\circ + x = 180^\circ$$ $$x = 180^\circ - 66^\circ$$ $$x = 114^\circ$$ 4. Explanation: The two angles are adjacent on a straight line, so their sum is $180^\circ$. Subtracting $66^\circ$ from $180^\circ$ gives $x$. --- 1. Problem: Find the unknown angle $x$ when two adjacent angles are $119^\circ$ and $x$. 2. Formula: Adjacent angles on a straight line sum to $180^\circ$. 3. Work: $$119^\circ + x = 180^\circ$$ $$x = 180^\circ - 119^\circ$$ $$x = 61^\circ$$ 4. Explanation: The two angles are adjacent on a straight line, so their sum is $180^\circ$. Subtracting $119^\circ$ from $180^\circ$ gives $x$.