Question

1. a= x + 23 80° 4x + 17

Explanation:

Step1: Apply exterior - angle theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $4x + 17=(x + 23)+80$.

Step2: Simplify the equation

First, expand the right - hand side: $4x+17=x + 23+80$. Then combine like terms: $4x+17=x + 103$.

Step3: Solve for x

Subtract x from both sides: $4x - x+17=x - x + 103$, which gives $3x+17 = 103$. Then subtract 17 from both sides: $3x+17 - 17=103 - 17$, so $3x=86$. Divide both sides by 3: $x=\frac{86}{3}$.

Step4: Find angle A

Angle $A=x + 23$. Substitute $x=\frac{86}{3}$ into the expression for angle A: $A=\frac{86}{3}+23=\frac{86}{3}+\frac{69}{3}=\frac{86 + 69}{3}=\frac{155}{3}\approx51.67^{\circ}$.

Answer:

$\frac{155}{3}^{\circ}$