Question

what is the value of a? a + 47° 3a - 17° 2a a = °

Explanation:

Step1: Apply angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. For the large triangle, we can set up an equation using the given angle expressions. The three angles of the large triangle are \(2a\), \(3a - 17\), and the third angle which is equal to \(180-(a + 47)\) (since the non - adjacent interior angle of the small triangle and \(a + 47\) are supplementary).
The sum of the angles of the large triangle gives us the equation: \(2a+(3a - 17)+(180-(a + 47))=180\).

Step2: Simplify the left - hand side of the equation

First, expand the equation: \(2a+3a - 17+180 - a - 47 = 180\).
Combine like terms: \((2a+3a - a)+(-17 + 180-47)=180\).
\(4a+(180-(17 + 47))=180\).
\(4a+(180 - 64)=180\).
\(4a + 116=180\).

Step3: Solve for \(a\)

Subtract 116 from both sides of the equation: \(4a=180 - 116\).
\(4a = 64\).
Divide both sides by 4: \(a=\frac{64}{4}\).

Answer:

\(a = 16\)