Question

the measures of the angles of a triangle are shown in the figure below. find the smallest angle.

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $(4x - 7)+(3x - 15)+90=180$.

Step2: Combine like - terms

$(4x+3x)+(-7 - 15)+90 = 180$, which simplifies to $7x-22 + 90=180$, then $7x + 68=180$.

Step3: Solve for x

Subtract 68 from both sides: $7x=180 - 68$, so $7x=112$. Divide both sides by 7: $x = 16$.

Step4: Find the measures of the non - right angles

For the angle $(4x - 7)^{\circ}$, substitute $x = 16$: $4\times16-7=64 - 7=57^{\circ}$.
For the angle $(3x - 15)^{\circ}$, substitute $x = 16$: $3\times16-15=48 - 15=33^{\circ}$.

Answer:

$33^{\circ}$