To find the missing angle in each triangle, we use the rule that
the sum of all interior angles in a triangle is always 180°.
We will solve each problem step by step:
1) Triangle TUV
* Given angles: $37^\circ$ and $63^\circ$.
* Add them together: $37 + 63 = 100$.
* Subtract from 180: $180 - 100 = 80$.
*
$m\angle U = 80^\circ$
2) Triangle ABC
* Given angles: The square symbol at C means it is a right angle ($90^\circ$), and angle A is $46^\circ$.
* Add them together: $90 + 46 = 136$.
* Subtract from 180: $180 - 136 = 44$.
*
$m\angle B = 44^\circ$
3) Triangle PQR
* Given angles: $51^\circ$ and $36^\circ$.
* Add them together: $51 + 36 = 87$.
* Subtract from 180: $180 - 87 = 93$.
*
$m\angle Q = 93^\circ$
4) Triangle EFG
* Given angles: $86^\circ$ and $47^\circ$.
* Add them together: $86 + 47 = 133$.
* Subtract from 180: $180 - 133 = 47$.
*
$m\angle F = 47^\circ$
5) Triangle XYZ
* Given angles: $118^\circ$ and $33^\circ$.
* Add them together: $118 + 33 = 151$.
* Subtract from 180: $180 - 151 = 29$.
*
$m\angle Y = 29^\circ$
6) Triangle UVW
* Given angles: $42^\circ$ and $64^\circ$.
* Add them together: $42 + 64 = 106$.
* Subtract from 180: $180 - 106 = 74$.
*
$m\angle V = 74^\circ$
7) Triangle KLM
* Given angles: $60^\circ$ and $60^\circ$.
* Add them together: $60 + 60 = 120$.
* Subtract from 180: $180 - 120 = 60$.
*
$m\angle K = 60^\circ$
8) Triangle STU
* Given angles: $35^\circ$ and $35^\circ$.
* Add them together: $35 + 35 = 70$.
* Subtract from 180: $180 - 70 = 110$.
*
$m\angle U = 110^\circ$
9) Triangle CDE
* Given angles: $53^\circ$ and $77^\circ$.
* Add them together: $53 + 77 = 130$.
* Subtract from 180: $180 - 130 = 50$.
*
$m\angle C = 50^\circ$
Final Answer:
1) $m\angle U = 80^\circ$
2) $m\angle B = 44^\circ$
3) $m\angle Q = 93^\circ$
4) $m\angle F = 47^\circ$
5) $m\angle Y = 29^\circ$
6) $m\angle V = 74^\circ$
7) $m\angle K = 60^\circ$
8) $m\angle U = 110^\circ$
9) $m\angle C = 50^\circ$
Parent Tip: Review the logic above to help your child master the concept of triangle interior angles worksheet.
