find the value of x in each case
Answers
2).=3x+40+11x-60+4x=180
=8x-4x+100=180
=4x=180-100
x=80/4
x=20
3).7x+3x+100=180
10x+100=180
10x=180-100
x=80/10
x=8
4).48+30+x=180
78+x=180
x=180-78
x=102
and make it brainleist
Given:
The attached figure
To Find:
The value of x in each case
Solution:
Before solving we should know that,
The sum of every angle in a triangle is 180 degrees.
The sum of supplementary angles is equal to 180 degrees.
When two lines intersect then the opposite angles are equal.
Now using this information we can start solving the value of x in each case,
(i) In triangle ABC the measure of the third angle using the sum of all angles of a triangle will be,
ACB+60+45=180
ACB=180-105
ACB=75
Now angle ACB will be equal to angle DCE because the lines intersect each other,
ACB=DCE=75
Now in triangle DCE using the property of the sum of angles of a triangle we have,
80+x+75=180
x=180-155
x=25
Hence, the value of x is 25 degrees.
(ii) angle DBC and ABC are supplementary angles so their sum will be equal to 180, we have
11x-60+ABC=180
ABC=240-11x
Now in triangle ABC, we use the property of sum of angles of a triangle,
240-11x+3x+40+4x=180
280-4x=180
4x=100
x=25
Hence, the value of x is 25 degrees.
(iii) The value of two interior angles will be,
1+100=180
1=80
And,
2+7x=180
2=180-7x
Now in the triangle using the property of sum of angles,
80+180-7x+3x=180
4x=80
x=20
Hence, the value of x is 20 degrees.
(iv) In triangle POT the two angles are 30 and 90 so the 3rd angle will be,
POT=180-90-30
POT=60
so angle POT and QOS will be equal than in triangle QOS,
48+60+x=180
x=72
Hence, the value of x is 72 degrees.