Question

one angle of a triangle is 55° greater than the smallest angle, and the third angle is 35° less than two - the smallest angle. find the measures of the three angles. the measure of the smallest angle is °

Explanation:

Step1: Let the smallest angle be $x$.

Let the smallest angle be $x$. Then the second - angle is $x + 55^{\circ}$, and the third - angle is $2x-35^{\circ}$.

Step2: Use the angle - sum property of a triangle.

The sum of the interior angles of a triangle is $180^{\circ}$. So, $x+(x + 55^{\circ})+(2x-35^{\circ})=180^{\circ}$.

Step3: Simplify the left - hand side of the equation.

Combine like terms: $(x+x + 2x)+(55^{\circ}-35^{\circ})=180^{\circ}$, which gives $4x+20^{\circ}=180^{\circ}$.

Step4: Solve for $x$.

Subtract $20^{\circ}$ from both sides: $4x=180^{\circ}-20^{\circ}=160^{\circ}$. Then divide both sides by 4: $x = 40^{\circ}$.

Step5: Find the other two angles.

The second angle is $x + 55^{\circ}=40^{\circ}+55^{\circ}=95^{\circ}$.
The third angle is $2x-35^{\circ}=2\times40^{\circ}-35^{\circ}=80^{\circ}-35^{\circ}=45^{\circ}$.

Answer:

The measures of the three angles are $40^{\circ}$, $95^{\circ}$, and $45^{\circ}$.