Question

angle addition postulate
m<qnp = 78°
(5x - 3)°
(3x - 7)°
find x
find m∠qnm

Explanation:

Step 1: Apply angle - addition postulate

By the angle - addition postulate, $m\angle QNP=m\angle QNM + m\angle MNP$. So, $(5x - 3)+(3x - 7)=78$.

Step 2: Simplify the left - hand side of the equation

Combine like terms: $5x+3x-3 - 7=78$, which simplifies to $8x-10 = 78$.

Step 3: Solve for $x$

Add 10 to both sides of the equation: $8x-10 + 10=78 + 10$, getting $8x=88$. Then divide both sides by 8: $x=\frac{88}{8}=11$.

Step 4: Find $m\angle QNM$

Substitute $x = 11$ into the expression for $m\angle QNM$. $m\angle QNM=5x-3=5\times11-3=55 - 3=52$.

Answer:

$x = 11$
$m\angle QNM=52^{\circ}$