Question

gardening a gardener uses a grow light to grow vegetables indoors. if ( mangle1 = 8x^{circ} ) and ( mangle2=(7x - 4)^{circ} ), what is ( mangle1 )?
example 3
find each measure.

1. ( mangle1 )
2. ( mangle2 )

Explanation:

Step1: Find the value of \(x\)

Since \(\angle1\) and \(116^{\circ}\) are supplementary (they form a linear - pair), \(m\angle1 + 116^{\circ}=180^{\circ}\). Also, \(m\angle1 = 8x^{\circ}\), so \(8x+116 = 180\).
Subtract 116 from both sides: \(8x=180 - 116\), \(8x = 64\).
Divide both sides by 8: \(x=\frac{64}{8}=8\).

Step2: Calculate \(m\angle1\)

Substitute \(x = 8\) into the formula for \(m\angle1\). Since \(m\angle1=8x^{\circ}\), then \(m\angle1=8\times8^{\circ}\).

Answer:

\(m\angle1 = 64^{\circ}\)