Question 5(multiple choice worth 6 points) (05.03 mc) the figure below shows a quadrilateral abcd with diagonal bd bisecting angle adc: a quadrilateral abcd is drawn with bd as a diagonal. bd bisects angle adc and forms two triangles abd and cbd. ad and cd are equal in length. which equation is true? angle dcb = angle adb angle dab = angle dcb angle abd = angle bcd angle abd = angle cdb

2.

Step-by-step explanation:

We have been given a diagram of a quadrilateral ABCD with diagonal BD bisecting angle ADC, which means that .

We can see that diagonal BD has divided quadrilateral ABCD into two triangles. We can see that in triangles ADB and CDB side AD equals to side CD and side BD equals to itself, therefore, triangles ADB and CDB are congruent by SAS postulate of congruence.  

Since triangle ADB is congruent to triangle CDB, therefore, all sides and angles of triangle ADB will be congruent to corresponding sides and angles of triangle CDB.

Let us see which of our given options represent corresponding angles of both triangles.

1.

We can see from our diagram that angle DAB corresponds to angle DCB, therefore, 1st equation is not true.

2.

We can see from our diagram that angle DAB corresponds to angle DCB, therefore, 2nd equation is true.

3.

We can see from our diagram that angle CBD corresponds to angle ABD, therefore, 3rd equation is not true.

4.

We can see from our diagram that angle CDB corresponds to angle ADB, therefore, 4th equation is not true.  

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

d. 145*2 is 290 than the total angle is 360 then minus 290 then divide by two