QUESTION IMAGE
Question
consider the figure below. given: ∠a = 6x + 19 ∠b = 4x - 3
Response
- Explanation:
- Step 1: Identify the relationship between the angles
- Since the two - angles \(A\) and \(B\) are complementary (as they form a right - angle, \(90^{\circ}\)), we know that \(\angle A+\angle B = 90^{\circ}\).
- Substitute the given expressions for \(\angle A\) and \(\angle B\) into the equation: \((6x + 19)+(4x-3)=90\).
- Step 2: Simplify the left - hand side of the equation
- Combine like terms: \(6x+4x+19 - 3=90\).
- \(10x + 16=90\).
- Step 3: Solve for \(x\)
- Subtract 16 from both sides of the equation: \(10x=90 - 16\).
- \(10x=74\).
- Divide both sides by 10: \(x=\frac{74}{10}=7.4\).
- Step 4: Find the measure of \(\angle A\) and \(\angle B\)
- For \(\angle A\): Substitute \(x = 7.4\) into the expression for \(\angle A\), \(\angle A=6x + 19=6\times7.4+19\).
- First, calculate \(6\times7.4 = 44.4\), then \(44.4+19=63.4^{\circ}\).
- For \(\angle B\): Substitute \(x = 7.4\) into the expression for \(\angle B\), \(\angle B=4x-3=4\times7.4 - 3\).
- First, calculate \(4\times7.4 = 29.6\), then \(29.6-3 = 26.6^{\circ}\).
- Answer: \(x = 7.4\), \(\angle A=63.4^{\circ}\), \(\angle B = 26.6^{\circ}\)
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- Explanation:
- Step 1: Identify the relationship between the angles
- Since the two - angles \(A\) and \(B\) are complementary (as they form a right - angle, \(90^{\circ}\)), we know that \(\angle A+\angle B = 90^{\circ}\).
- Substitute the given expressions for \(\angle A\) and \(\angle B\) into the equation: \((6x + 19)+(4x-3)=90\).
- Step 2: Simplify the left - hand side of the equation
- Combine like terms: \(6x+4x+19 - 3=90\).
- \(10x + 16=90\).
- Step 3: Solve for \(x\)
- Subtract 16 from both sides of the equation: \(10x=90 - 16\).
- \(10x=74\).
- Divide both sides by 10: \(x=\frac{74}{10}=7.4\).
- Step 4: Find the measure of \(\angle A\) and \(\angle B\)
- For \(\angle A\): Substitute \(x = 7.4\) into the expression for \(\angle A\), \(\angle A=6x + 19=6\times7.4+19\).
- First, calculate \(6\times7.4 = 44.4\), then \(44.4+19=63.4^{\circ}\).
- For \(\angle B\): Substitute \(x = 7.4\) into the expression for \(\angle B\), \(\angle B=4x-3=4\times7.4 - 3\).
- First, calculate \(4\times7.4 = 29.6\), then \(29.6-3 = 26.6^{\circ}\).
- Answer: \(x = 7.4\), \(\angle A=63.4^{\circ}\), \(\angle B = 26.6^{\circ}\)