Chapter 11.6, Problem 49SR

To determine

To calculate: Measure of the angle $x^{°}$

Answer to Problem 49SR

100 degree $\left(i.e{.100}^{°}\right)$

Explanation of Solution

Given information:Three angles of a parallelogram are given as: 60°, 105° and 95°

Formula used:

The sum of angles of a regular polygon may be represented as:

Sum of angles = $\left(n-2\right)\times 180$

Where, n = number of sides of the regular polygon.

  $\therefore$ Sum of angles of a quadrilateral = $\left(4-2\right)\times 180$

= $2\times 180={360}^{°}$

Calculation:

Now, we have

  $x+60+105+95=360$

  $\Rightarrow x+260=360$

  $\Rightarrow x=360-260$

  $\therefore x={100}^{°}$