Answer:
- Equation: 4x +(x -5) = 90
- ∠1 = 76°
- ∠2 = 14°
Explanation:
Given two complementary angles labeled (4x)° and (x-5)°, you want an equation for finding x, and the measures of the two angles.
Equation
The equation will reflect the fact that the angles have a sum of 90°:
4x +(x -5) = 90
Solution
The equation simplifies to ...
5x -5 = 90
5x = 95
x = 19
∠1 = 4x° = 76° . . . . . . measure of larger angle
∠2 = (x -5)° = 14° . . . . . measure of smaller angle
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Additional comment
The little square at the vertex of the angles means that is a right-angle corner. Its measure is 90°. The two angles 1 and 2 together make up that right angle. That is the relation you use to form the equation.
Rewriting (simplifying) the sum ...
4x +(x -5) = 5x -5
tells you nothing about the value of x. Any value for x will satisfy this equation. In order to find x, you need to relate this sum to something other than itself. (There is a reason why the angle is marked as a right angle.)