Question

using the image provided, find m∠bac. 82° 85° 74° 80°

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, $(x + 47)+(3x - 1)=154$.

Step2: Simplify the left - hand side

Combine like terms: $x+3x + 47-1=154$, which gives $4x+46 = 154$.

Step3: Solve for x

Subtract 46 from both sides: $4x=154 - 46$, so $4x = 108$. Then divide both sides by 4: $x=\frac{108}{4}=27$.

Step4: Find the measure of $\angle BAC$

Substitute $x = 27$ into the expression for $\angle BAC$ which is $x + 47$. So, $m\angle BAC=27 + 47=74^{\circ}$.

Answer:

$74^{\circ}$