Question

find the measure of ∠a. (5x - 27)° (7x - 26)° (10x - 23)°

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $(5x - 27)+(7x - 26)+(10x - 23)=180$.

Step2: Combine like - terms

$(5x+7x + 10x)+(-27-26 - 23)=180$, which simplifies to $22x-76 = 180$.

Step3: Isolate the variable term

Add 76 to both sides of the equation: $22x=180 + 76$, so $22x=256$.

Step4: Solve for x

Divide both sides by 22: $x=\frac{256}{22}=\frac{128}{11}\approx11.64$.

Step5: Find the measure of $\angle A$

$\angle A=(5x - 27)$. Substitute $x = \frac{128}{11}$ into the expression: $\angle A=5\times\frac{128}{11}-27=\frac{640}{11}-27=\frac{640-297}{11}=\frac{343}{11}\approx31.18^{\circ}$.

Answer:

$\frac{343}{11}$ degrees (or approximately $31.18^{\circ}$)