Question

24. ABCDE and PQRST are regular pentagons.

Answer 1

Answer:

126°

Step-by-step explanation:

In quadrilateral DSRC, SR || DC (given)

AP = BQ = CR = DS = ET (given)

$\therefore$ CR bisects $\angle DCB$

$\therefore m\angle DCR=\frac{108\degree}{2}$

($108\degree$ is the measure of an angle of pentagon)

$\therefore m\angle DCR=54\degree$

$\because m\angle DCR + m\angle SRC=180\degree$

(Measure of interior angles on the same side of transversal)

$\therefore 54\degree + m\angle SRC=180\degree$

$\therefore m\angle SRC=180\degree- 54\degree$

$\therefore m\angle SRC=126\degree$