Question

given the following triangle, find the angles in degrees (the two angles are 2x + 1 and 3x + 4).

Explanation:

Step1: Use the property of right - angled triangle

In a right - angled triangle, the sum of the two non - right angles is \(90^{\circ}\). So, \((2x + 1)+(3x + 4)=90\).

Step2: Solve the equation for \(x\)

Combine like terms: \(2x+3x+1 + 4=90\), which simplifies to \(5x+5 = 90\).
Subtract \(5\) from both sides: \(5x=90 - 5=85\).
Divide both sides by \(5\): \(x=\frac{85}{5}=17\).

Step3: Find the two non - right angles

For the first angle: \(2x+1\), substitute \(x = 17\). Then \(2\times17+1=34 + 1=35\).
For the second angle: \(3x+4\), substitute \(x = 17\). Then \(3\times17+4=51+4=55\).

Answer:

B. 35, 90, 55