Question

m∠a =
8
a
(5x - 27)°
(10x - 23)°
c
b
(7x - 26)°

Explanation:

Step1: Recall 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: \(22x-76 + 76=180 + 76\), resulting in \(22x=256\).

Step4: Solve for x

Divide both sides by 22: \(x=\frac{256}{22}=\frac{128}{11}\).

Step5: Find the measure of angle A

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

Answer:

\(\frac{343}{11}\) degrees