Question

use the figure below to answer question #13 - 14. let m∠mqp = 80.
#13: m∠mqn=
your answer
#14: m∠nqp=
your answer

Explanation:

Step1: Set up an equation

Since $\angle MQP=\angle MQN+\angle NQP$, we have $(6x - 3)+(4x + 3)=80$.
Combining like - terms: $6x+4x-3 + 3=80$, which simplifies to $10x=80$.

Step2: Solve for x

Dividing both sides of the equation $10x = 80$ by 10, we get $x=\frac{80}{10}=8$.

Step3: Find $\angle MQN$

Substitute $x = 8$ into the expression for $\angle MQN$, which is $6x-3$.
$6x-3=6\times8 - 3=48-3 = 45$.

Step4: Find $\angle NQP$

Substitute $x = 8$ into the expression for $\angle NQP$, which is $4x + 3$.
$4x+3=4\times8+3=32 + 3=35$.

Answer:

#13: 45
#14: 35