Two lines intersect and form angles 4m-15 and m+75. Find m.

Hey Elzy, good to see you again. Let's break down this geometry problem step by step. Problem 1: Find the value of m in the diagram below. The diagram shows two straight lines intersecting. When two lines intersect, they form pairs of vertically opposite angles. Vertically opposite angles are angles that are opposite each other at the intersection point, and they are always equal. The two angles given are 4m - 15 and m + 75. These are vertically opposite angles. Step 1: Set up the equation. Since vertically opposite angles are equal, we can set the expressions for the two angles equal to each other. 4m - 15 = m + 75 Step 2: Group like terms. To solve for m, we need to get all terms with m on one side of the equation and all constant terms on the other side. Subtract m from both sides and add 15 to both sides. 4m - m = 75 + 15 Step 3: Simplify the equation. Combine the terms on each side. 3m = 90 Step 4: Solve for m. Divide both sides by 3 to isolate m. (3m)/(3) = (90)/(3) m = 30 The value of m is 30. To check your answer, substitute m=30 back into the original angle expressions: Angle 1: 4(30) - 15 = 120 - 15 = 105^ Angle 2: 30 + 75 = 105^ Since both angles are 105^, our value for m is correct. The final answer is 30. What's next? 📸