Question

find the value of a given the following figure.
(a + 30)°
129° (5a - 4)°
o a. a = 4.17
o b. a = 3.17
o c. a = 7.14
o d. a = 7.13

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \((a + 30)+129+(5a - 4)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((a+5a)+(30 + 129-4)=180\), which gives \(6a+155 = 180\).

Step3: Isolate the variable \(a\)

Subtract 155 from both sides: \(6a=180 - 155\), so \(6a = 25\). Then divide both sides by 6: \(a=\frac{25}{6}\approx4.17\).

Answer:

A. a = 4.17