Questions: The second angle of a triangular kite is four times as large as the first. The third angle is 5° more than the sum of the other two angles. Find the measure of the second angle. The measure of the second angle is .

Solution Steps

To solve this problem, we need to use the fact that the sum of the angles in a triangle is always \(180^\circ\). Let's denote the first angle as \(x\). According to the problem, the second angle is four times the first angle, so it is \(4x\). The third angle is \(5^\circ\) more than the sum of the first two angles, so it is \(x + 4x + 5\). We can set up an equation using these expressions and solve for \(x\). Once we find \(x\), we can easily find the second angle by calculating \(4x\).

Let the first angle of the triangle be \( x \). According to the problem, the second angle is four times the first angle, so it is \( 4x \). The third angle is \( 5^\circ \) more than the sum of the first two angles, which can be expressed as \( x + 4x + 5 \).

The sum of the angles in a triangle is always \( 180^\circ \). Therefore, we can set up the equation: \[ x + 4x + (x + 4x + 5) = 180 \]

Simplify the equation: \[ 10x + 5 = 180 \] Subtract 5 from both sides: \[ 10x = 175 \] Divide both sides by 10 to solve for \( x \): \[ x = 17.5 \]

The second angle is four times the first angle: \[ 4x = 4 \times 17.5 = 70 \]

Final Answer