Let's solve each part of this worksheet step by step.
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Section A: Calculate the missing angles in these right angles.
In a
right angle, the total is
90°. So, if one angle is given, we subtract it from 90° to find the missing angle.
---
1.
a°:
Given: 25°
$ a = 90^\circ - 25^\circ = \boxed{65^\circ} $
2.
b°:
Given: 15°
$ b = 90^\circ - 15^\circ = \boxed{75^\circ} $
3.
c°:
Given: 80°
$ c = 90^\circ - 80^\circ = \boxed{10^\circ} $
4.
d°:
Given: 72°
$ d = 90^\circ - 72^\circ = \boxed{18^\circ} $
5.
e°:
Given: 34°
$ e = 90^\circ - 34^\circ = \boxed{56^\circ} $
6.
f°:
This is a right angle split into two parts: 19° and f°.
$ f = 90^\circ - 19^\circ = \boxed{71^\circ} $
---
Section B: Calculate the missing angles on these straight lines.
On a
straight line, angles add up to
180°.
---
7.
g°:
Given: 45°
$ g = 180^\circ - 45^\circ = \boxed{135^\circ} $
8.
h°:
Given: 128°
$ h = 180^\circ - 128^\circ = \boxed{52^\circ} $
9.
i°:
Given: 104°
$ i = 180^\circ - 104^\circ = \boxed{76^\circ} $
10.
j°:
Three angles on a straight line: 71°, 48°, and j°
$ j = 180^\circ - (71^\circ + 48^\circ) = 180^\circ - 119^\circ = \boxed{61^\circ} $
11.
k°:
Angles on a straight line: k°, 90° (right angle), and 11°
$ k = 180^\circ - (90^\circ + 11^\circ) = 180^\circ - 101^\circ = \boxed{79^\circ} $
12.
l°:
Given: 43°
$ l = 180^\circ - 43^\circ = \boxed{137^\circ} $
13.
m°:
Angles around a point on a straight line: 25°, m°, 78°
$ m = 180^\circ - (25^\circ + 78^\circ) = 180^\circ - 103^\circ = \boxed{77^\circ} $
14.
n°:
There’s a right angle (90°), 16°, and n° on a straight line.
$ n = 180^\circ - (90^\circ + 16^\circ) = 180^\circ - 106^\circ = \boxed{74^\circ} $
15.
p°:
Right angle (90°), 66°, and p° on a straight line?
Wait — actually, it looks like three angles meeting at a point on a straight line:
One is 66°, one is 90°, and p° is the remaining.
But note: the vertical line and horizontal line form a right angle, and p° is above that.
The total around the point on the straight line must be 180°.
So:
$ p = 180^\circ - (90^\circ + 66^\circ) = 180^\circ - 156^\circ = \boxed{24^\circ} $
16.
q°:
Three equal angles labeled q° on a straight line:
$ 3q = 180^\circ $
$ q = \frac{180^\circ}{3} = \boxed{60^\circ} $
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✔ Final Answers:
####
Section A
- $ a^\circ = 65^\circ $
- $ b^\circ = 75^\circ $
- $ c^\circ = 10^\circ $
- $ d^\circ = 18^\circ $
- $ e^\circ = 56^\circ $
- $ f^\circ = 71^\circ $
####
Section B
- $ g^\circ = 135^\circ $
- $ h^\circ = 52^\circ $
- $ i^\circ = 76^\circ $
- $ j^\circ = 61^\circ $
- $ k^\circ = 79^\circ $
- $ l^\circ = 137^\circ $
- $ m^\circ = 77^\circ $
- $ n^\circ = 74^\circ $
- $ p^\circ = 24^\circ $
- $ q^\circ = 60^\circ $
---
🔍 Explanation Summary:
-
Right angles = 90° → subtract known angle.
-
Straight lines = 180° → subtract known angles from 180°.
- When multiple angles are on a straight line, sum them and subtract from 180°.
- For
equal angles on a straight line, divide 180° by the number of equal parts.
Let me know if you'd like a visual explanation or printable version!
Parent Tip: Review the logic above to help your child master the concept of calculating angles worksheet.
