  Content: We present the results from $Suzaku$ observations of the merging
cluster of galaxies CIZA J2242.8+5301 at $z$=0.192. Aims. To study the physics
of gas heating and particle acceleration in cluster mergers, we investigated
the X-ray emission from CIZA J2242.8+5301, which hosts two giant radio relics
in the northern/southern part of the cluster. Methods. We analyzed data from
three-pointed Suzaku observations of CIZA J2242.8+5301 to derive the
temperature distribution in four different directions. Results: The
Intra-Cluster Medium (ICM) temperature shows a remarkable drop from
8.5$_{-0.6}^{+0.8}$ keV to 2.7$_{-0.4}^{+0.7}$ keV across the northern radio
relic. The temperature drop is consistent with a Mach number ${\cal
M}_n=2.7^{+0.7}_{-0.4}$ and a shock velocity
$v_{shock:n}=2300_{-400}^{+700}\rm\,km\,s^{-1}$. We also confirm the
temperature drop across the southern radio relic. However, the ICM temperature
beyond this relic is much higher than beyond the northern one, which gives a
Mach number ${\cal M}_s=1.7^{+0.4}_{-0.3}$ and shock velocity
$v_{shock:s}=2040_{-410}^{+550}\rm \,km\,s^{-1}$. These results agree with
other systems showing a relationship between the radio relics and shock fronts
which are induced by merging activity. We compare the X-ray derived Mach
numbers with the radio derived Mach numbers from the radio spectral index under
the assumption of diffusive shock acceleration in the linear test particle
regime. For the northern radio relic, the Mach numbers derived from X-ray and
radio observations agree with each other. Based on the shock velocities, we
estimate that CIZA J2242.8+5301 is observed approximately 0.6 Gyr after core
passage. The magnetic field pressure at the northern relic is estimated to be
9% of the thermal pressure.
