# Given: prst is a parallelogram m∠t: m∠r=1: 3, rd ⊥ ps , rm ⊥ st find: m∠drm

∠DRM=45°

Step-by-step explanation:

Given: PRST is a parallelogram, m∠T:m∠R=1:3, RD ⊥ PS , RM ⊥ ST.

To find: m∠DRM

Solution: Since, PRST is a parallelogram and then let m∠T=x then m∠R=3x.

From the figure, we get that m∠T+m∠R=180°(Adjacent angles)

x+3x=180°

x=45°

Therefore, m∠T=45° and m∠R=135°.

Also, in parallelogram, opposite angles are equal, therefore m∠R=m∠S=135°.

Now, We know that sum of all the angles of the parallelogram =360°, then

From the quadrilateral DRMS,

∠DRM+∠RMS+∠MSD+∠SDR=360°

∠DRM+90°+135°+90°=360°

∠DRM=360°-315°

∠DRM=45°

d. 9

step-by-step explanation:

in the table given in the picture, x is the input of the function and f(x) is the output on the given input. in the given table, it can be read as the value of function at -3 is it's respective value of f(x) which is -9.

as we have to find the value of f(3), we will see that what is the value of output on input 3. we can see in the table that the output value at x=3 is 9.

so, option d is the correct answer ..

answer: 5

step-by-step explanation: