Answer:
[tex]m\angle PTR = 70[/tex]
[tex]m\angle 1 = 34[/tex]
Step-by-step explanation:
Solving (1):
Given: Trapezium APTR
Find [tex]m\angle PTR[/tex]
In the trapezium:
[tex]AR = PT[/tex]
And AP is parallel to RT.
This implies that:
[tex]m\angle APT = m\angle RAP =110[/tex] and [tex]m\angle PTR = m\angle TRA[/tex]
The sum of all angles is:
[tex]m\angle APT + m\angle RAP + m\angle PTR + m\angle TRA = 360[/tex]
[tex]110 + 110 + m\angle PTR + m\angle TRA = 360[/tex]
Recall that:
[tex]m\angle PTR = m\angle TRA[/tex]
[tex]110 + 110 + m\angle PTR + m\angle PTR = 360[/tex]
[tex]220 + 2m\angle PTR = 360[/tex]
[tex]2m\angle PTR = 360 - 220[/tex]
[tex]2m\angle PTR = 140[/tex]
Divide by 2
[tex]m\angle PTR = 70[/tex]
Solving (2):
Given
[tex]m\angle 1 = 3x + 4[/tex]
[tex]m\angle 2 = x + 24[/tex]
Required
Find [tex]m\angle 1[/tex]
Both angles are vertically opposie:
So:
[tex]m\angle 1 =m\angle 2[/tex]
[tex]3x + 4= x + 24[/tex]
Collect Like Terms
[tex]3x -x= 24 - 4[/tex]
[tex]2x = 20[/tex]
[tex]x = 10[/tex]
So:
[tex]m\angle 1 = 3x + 4[/tex]
[tex]m\angle 1 = 3 * 10 + 4[/tex]
[tex]m\angle 1 = 30 + 4[/tex]
[tex]m\angle 1 = 34[/tex]
