The values of the lettered angles in the figures are:
i) x = 50⁰
ii) a = 45⁰
iii) a = 52⁰
iv) a = 65⁰, b = 128⁰ and c = 27⁰
How to find the value of lettered angles in a figure.
I)Fig1
In the triangle
60 + 70 + x = 180(sum of angles in a ∆ postulate)
130 + x = 180
x = 180 - 130
= 50⁰
ii) 25 + 110 + angleA = 180⁰(sum of angles in a ∆)
135 + angleA = 180
angleA = 180 - 135
= 45⁰
a = angleA (vertical angles theorem)
a = 45⁰
iii) Given two parallel lines
The 3rd angle in the triangle is equals to 78⁰ (alt. angles postulate)
Therefore,
50 + 78 + a = 180(angles in a triangle)
128 + a = 180
a = 180 - 128
= 52⁰
iv) In the issoceles triangle
a + a + 50 = 180
2a + 50 = 180
2a = 180 - 50
2a = 130
a = 130/2
= 65⁰
a + b = 180(alt. angles and linear angles postulates)
b = 180 - a
= 180 -52
= 128⁰
25 + c = a( 2 int. angles equals 1 opp. ext. angle)
25 + c = 52
c = 52 - 25
= 27⁰
Therefore, the values of the lettered angles are:
i) x = 50⁰
ii) a = 45⁰
iii) a = 52⁰
iv) a = 65⁰, b = 128⁰ and c = 27⁰