Chapter 11.3, Problem 51STP

To determine

To find: The value of ‘x’ & ‘ $\angle MTQ\text{ \& }\angle PTM$ ’.

Answer to Problem 51STP

The value of x = 56º

  $\begin{array}{l}\angle MTQ=117°\\ \angle PTM=63°\end{array}$

Explanation of Solution

Given Information:

Two lines MN and PQ intersect at point T, where the measure of the angles formed are $m\angle MTQ=2x+5$ and $m\angle PTM=x+7$ .

Figure:

  

Since lines MN and PQ are straight lines intersecting at T, they form a Linear Pair (i.e. Sum of angles is equal to 180º) on either sides of the given lines.

Therefore $\angle MTQ+\angle PTM=180°$

  $\begin{array}{l}\angle MTQ+\angle PTM=\left(2x+5\right)+\left(x+7\right)\\ \text{Thus}\\ \Rightarrow \left(2x+5\right)+\left(x+7\right)=180°\\ \Rightarrow 2x+x+5+7=180°\\ \Rightarrow 3x+12=180°\\ \Rightarrow 3x=180-12\\ \Rightarrow 3x=168°\\ \Rightarrow x=\frac{168}{3}=56°\\ \Rightarrow x=56°\end{array}$

Now,

  $\begin{array}{l}\angle MTQ=2x+5=2\left(56°\right)+5\\ \Rightarrow \angle MTQ=117°\\ \&\\ \angle PTM=x+7=56°+7\\ \Rightarrow \angle PTM=63°\end{array}$