Question

problem 19: (first taught in lesson 15) find ( mangle h ) and ( mangle k ) if the two angles are comple - mentary and if ( mangle h=2x - 1 ) and ( mangle k=8x - 9 ). after you enter your answer press go. ( mangle h= ) ( mangle k= )

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle H + m\angle K=90\). Substitute \(m\angle H = 2x - 1\) and \(m\angle K = 8x - 9\) into the equation: \((2x - 1)+(8x - 9)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+8x-1 - 9=90\), which simplifies to \(10x-10 = 90\).

Step3: Solve for \(x\)

Add \(10\) to both sides: \(10x-10 + 10=90 + 10\), so \(10x=100\). Divide both sides by \(10\): \(x=\frac{100}{10}=10\).

Step4: Find \(m\angle H\)

Substitute \(x = 10\) into \(m\angle H=2x - 1\). Then \(m\angle H=2\times10-1=20 - 1=19\).

Step5: Find \(m\angle K\)

Substitute \(x = 10\) into \(m\angle K=8x - 9\). Then \(m\angle K=8\times10-9=80 - 9=71\).

Answer:

\(m\angle H = 19\), \(m\angle K = 71\)