Question

1. in a triangle, the second angle is 40° larger than the first, and the third angle is 19° larger than the second. what is the size of the first angle? 19° 27° 59° 99°

Explanation:

Step1: Let the first angle be \(x\)

Let the first angle \(=x\). Then the second angle \(=x + 40\), and the third angle \(=(x + 40)+19=x+59\)

Step2: Use the triangle - angle sum formula

Since the sum of angles in a triangle is \(180^{\circ}\), we have \(x+(x + 40)+(x+59)=180\)

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Step3: Solve for \(x\)

Subtract \(99\) from both sides: \(3x=180 - 99=81\). Then divide both sides by \(3\): \(x=\frac{81}{3}=27\)

Answer:

\(27^{\circ}\)