Question

find the measure of the angle indicated. 23) find m∠t.

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $8x + 14=(6x - 2)+40$.

Step2: Solve the equation for x

First, simplify the right - hand side: $8x+14 = 6x+38$. Then, subtract $6x$ from both sides: $8x - 6x+14=6x - 6x + 38$, which gives $2x+14 = 38$. Next, subtract 14 from both sides: $2x+14 - 14=38 - 14$, so $2x = 24$. Divide both sides by 2: $x = 12$.

Step3: Find the measure of $\angle T$

Substitute $x = 12$ into the expression for $\angle T$. $\angle T=6x - 2$. So, $\angle T=6\times12 - 2=72 - 2=70^{\circ}$.

Answer:

$70^{\circ}$