Question

A field is in the shape of a pentagon as shown in the figure. Three of the interior angles of the pentagon are right angles. The remaining two interior angles are congruent. What is the measure of each angle?

Answer 1

$PQRST$ is a pentagon.

$Sumofallangleofanypolygonis(n-2){180}^o$ Where n= number of sides of Polygon

Sum of all angle of pentagon is ${540}^o$ degree

Here, $\angle P=\angle Q=\angle S={90}^o$ [ Given ]

$\Rightarrow$ Let $\angle T=\angle R=x$ [ Since both angles are congruent ]

$\Rightarrow$ $\angle P+\angle Q+\angle R+\angle S+\angle T={540}^o.$

$\Rightarrow$ ${90}^o+{90}^o+x+{90}^o+x={540}^o$

$\Rightarrow$ ${270}^o+2x={540}^o.$

$\Rightarrow$ $2x={270}^o$

$\Rightarrow$ $x={135}^o.$

$\therefore$ $\angle T=\angle R={135}^o.$