Question

point p is in the interior of ∠tus. if m∠tup = 2x - 41, m∠tus = 146°, and m∠sup = 4x - 23. find x and m∠tup. draw a diagram, then solve to answer the following questions. x = m∠tup = (remember degrees!)

Explanation:

Step1: Use angle - addition postulate

Since point $P$ is in the interior of $\angle TUS$, we know that $m\angle TUP + m\angle SUP=m\angle TUS$. Substitute the given angle - measures: $(2x - 41)+(4x - 23)=146$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side: $2x+4x-41 - 23 = 146$, which simplifies to $6x-64 = 146$.

Step3: Isolate the variable term

Add 64 to both sides of the equation: $6x-64 + 64=146 + 64$, so $6x=210$.

Step4: Solve for $x$

Divide both sides of the equation by 6: $\frac{6x}{6}=\frac{210}{6}$, and $x = 35$.

Step5: Find $m\angle TUP$

Substitute $x = 35$ into the expression for $m\angle TUP$: $m\angle TUP=2x-41=2\times35 - 41$. First, calculate $2\times35=70$, then $70-41 = 29$.

Answer:

$x = 35$
$m\angle TUP=29^{\circ}$