<h3><u>
Answer:</u></h3>
<h3>
<u>Step-by-step explanation:</u></h3>
A parallelogram is given to us . in which m ∠ B = 5x and m ∠C = 2x + 12 ° . And we need to find x .
<u>Figure</u><u> </u><u>:</u><u>-</u><u> </u>
<u>Q. no. 1 ) <em>Find</em><em> </em><em>the</em><em> </em><em>value</em><em> </em><em>of</em><em> </em><em>x</em><em>. </em></u>
Here we can clearly see that ∠DCB and ∠ABC are co - interior angles . And we know that the sum of co interior angles is 180° .
<h3>
<u>Hence</u><u> </u><u>the</u><u> value</u><u> of</u><u> x</u><u> is</u><u> </u><u>2</u><u>4</u><u>°</u><u> </u><u>.</u></h3>
<u>Q</u><u>.</u><u> </u><u>no</u><u>.</u><u> </u><u>2</u><u> </u><u>)</u><u> </u><u>Deter</u><u>mine</u><u> the</u><u> </u><u>meas</u><u>ure</u><u> </u><u>of</u><u> </u><u><</u><u> </u><u>C</u><u> </u><u>.</u>
Here we can see that <C = 2x + 12 ° . So ,
<h3>
<u>Hence</u><u> </u><u>the</u><u> value</u><u> of</u><u> </u><u><</u><u>C</u><u> </u><u>is</u><u> </u><u>6</u><u>0</u><u>°</u><u> </u><u>.</u></h3>
<u>Q</u><u>.</u><u> </u><u>no</u><u>.</u><u> </u><u>3</u><u> </u><u>)</u><u> </u><u>Deter</u><u>mine</u><u> the</u><u> measure</u><u> of</u><u> </u><u><</u><u> </u><u>D</u><u> </u><u>.</u><u>How</u><u> </u><u>you</u><u> </u><u>determi</u><u>ned</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>.</u>
Here we can clearly see that ∠D and ∠C are co - interior angles . And we know that the sum of co interior angles is 180° .
<h3>
<u>Hence</u><u> </u><u>the</u><u> value</u><u> of</u><u> </u><u><</u><u>D</u><u> </u><u>is</u><u> </u><u>1</u><u>2</u><u>0</u><u>°</u><u> </u><u>.</u></h3>