Question

angles a and b are complementary to each other. if ( mangle a = 23^{circ} ) and ( mangle b=(4x + 15)^{circ} ), find the value of ( x ).
( x = 2 )
( x = 13 )
( x = 35.5 )
( x = 67 )

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle A + m\angle B=90^{\circ}\).
Substitute \(m\angle A = 23^{\circ}\) and \(m\angle B=(4x + 15)^{\circ}\) into the equation: \(23+(4x + 15)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+(23 + 15)=90\), which simplifies to \(4x+38 = 90\).

Step3: Isolate the term with \(x\)

Subtract 38 from both sides: \(4x+38-38=90 - 38\). So, \(4x=52\).

Step4: Solve for \(x\)

Divide both sides by 4: \(x=\frac{52}{4}\).

Answer:

\(x = 13\)