Find the measure of $angle A C D$ .

30⁰
45⁰
60⁰
90⁰

hint Hint:

In this question, we have to find the value of $angle$ ACD if AC and BE are parallel pair of lines where $angle$ ABE = 120 $degree$ and $angle$ ADC = 90 $degree$ . As $angle$ ABE and $angle$ BAC are executive interior angles so, there sum would be 180 $degree$ and thus we get the value of $angle$ BAC. Later, as the sum of angles of triangles are 180 $degree$ so we can the value of $angle$ ACD .

The correct answer is: 30⁰

As we know that, $angle$ ABE and $angle$ CAB are consecutive interior angles,
so, $angle$ ABE + $angle$ CAB = 180 $degree$
120 $degree$ + $angle$ CAB = 180 $degree$
$angle$ CAB = 180 $degree$ - 120 $degree$
$angle$ CAB = 60 $degree$
Now, in $increment A D C comma space$
$angle$ ADC + $angle$ ACD + $angle$ DAC =180 $degree$
90 $degree$ + $angle$ ACD + 60 $degree$ =180 $degree$
$angle$ ACD = 180 $degree$ - 150 $degree$
$angle$ ACD = 30 $degree$
Hence, required value of $angle$ ACD is 30 $degree$ .

Line x passes through (2,3) and (7, -1). Line y passes through (5, 4) and (-3,2). Which line is steeper, x or y?

MathematicsGrade9

Grade9

Mathematics

If l || m then find the measures of x and y?

In this question we have to find x and y given that l is parallel to m and t is the transversal. First to find x we can use linear pair as we know that the sum of angles which are in linear pair is 180 deg. Next to find y we can use the theorem alternate exterior angles are equal.