in the following figures find the value of x and y
Answers
Answer:
in 1st triangle x = 50° and in 2nd triangle x= 33° and y= 82°
I hope it will help you
Answer:
Hope this helps you.
Step-by-step explanation:
Here, I will tell you the measures of all the angles in both the triangles.
A] First Figure (Triangle ABC)
(I) Measure of angle B:
Measure of exterior angle A = 107°
Measure of angle C = 57°
Law : The measure of exterior angle is equal to the sum of the remote interior angles.
.... Exterior angle property
Therefore, measure of angle B = x = 107 - 57 = 50
Therefore, x = 50°
(II) Measure of angle A = ?
Law : The sum of the measures of all angles of a triangle is 180°.
.... Angle sum property
Therefore, Measure of angle A = 180 - (57 + 50)
= 180 - 107
= 73°
(III) Measure of all angles of triangle ABC:
Angle A = 73°
Angle B = 50°
Angle C = 57°
Exterior Angle A = 107°
B] Second Figure (Triangle ABC)
(I) Triangle ADC:
Measure of angle A = 40°
Measure of angle D = 107°
Law : The sum of the measures of all angles of a triangle is 180°.
.... Angle sum property
Therefore, measure angle C = 180 - (107 + 40)
= 180 - 147
= 33°
(II) Measure of angle C:
Measure of (complete) angle C = x + 65
x = 33
Therefore, measure of angle C = 33 + 65
= 98°
(III) Measure of angle B:
Measure of angle A = 40°
Measure of angle C = 98°
Law : The sum of the measures of all angles of a triangle is 180°.
Law : The sum of the measures of all angles of a triangle is 180°. .... Angle sum property
Therefore, measure of angle B = 180 - (40 + 98)
= 180 - 138
= 42°
(IV) Measure of angle ECB :
Measure of angle ECB = y
Law : The measure of exterior angle is equal to the sum of the remote interior angles.
.... Exterior angle property
Therefore, measure of angle ECB = 40 + 42
= 82°