Question

1. type of angle pair: same - side exterior these angles are: choose your answer... equation: choose your answer... x = type your answer... measure of the 3x + 77 angle = type your answer... measure of the 4x + 54 angle = type your answer...

Explanation:

Step1: Recall angle - pair property

If two parallel lines are cut by a transversal, same - side exterior angles are supplementary. So the equation is $(3x + 77)+(4x + 54)=180$.

Step2: Combine like terms

$3x+4x+77 + 54=180$, which simplifies to $7x+131 = 180$.

Step3: Solve for x

Subtract 131 from both sides: $7x=180 - 131=49$. Then divide both sides by 7, so $x = 7$.

Step4: Find the measure of $3x + 77$

Substitute $x = 7$ into $3x+77$, we get $3\times7+77=21 + 77=98$.

Step5: Find the measure of $4x + 54$

Substitute $x = 7$ into $4x+54$, we get $4\times7+54=28 + 54=82$.

Answer:

These angles are: supplementary
Equation: $(3x + 77)+(4x + 54)=180$
$x = 7$
Measure of the $3x + 77$ angle $=98$
Measure of the $4x + 54$ angle $=82$