Question

question the measures of the angles of a triangle are shown in the figure below. solve for x. answer attempt 1 out of 2

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. In the given right - triangle, the three angles are 90°, (5x + 1)°, and (5x+19)°. So, we can write the equation: $(5x + 1)+(5x + 19)+90=180$.

Step2: Combine like terms

First, combine the x - terms and the constant terms on the left - hand side of the equation: $5x+5x+1 + 19+90=180$, which simplifies to $10x+110 = 180$.

Step3: Isolate the variable term

Subtract 110 from both sides of the equation: $10x+110−110=180−110$, resulting in $10x=70$.

Step4: Solve for x

Divide both sides of the equation by 10: $\frac{10x}{10}=\frac{70}{10}$, so $x = 7$.

Answer:

$x = 7$