Question

in the diagram, ( z^{circ} ) and ( y^{circ} ) are the measures of two complementary angles. also, the measure of one of the angles is ( 29.6^{circ} ). what is the correct value for ( x )? enter your answer as a decimal, if necessary, like this: 42.5

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles sum to \(90^{\circ}\). So \(z + y=90^{\circ}\).

Step2: Recall the definition of a straight - angle

A straight - angle is \(180^{\circ}\). So \(x+z + y+29.6^{\circ}=180^{\circ}\).

Step3: Substitute \(z + y\) into the straight - angle equation

Since \(z + y = 90^{\circ}\), substitute into \(x+(z + y)+29.6^{\circ}=180^{\circ}\). We get \(x+90^{\circ}+29.6^{\circ}=180^{\circ}\).

Step4: Solve for \(x\)

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Answer:

\(60.4\)