Angle Quest Worksheet
Geometry Review Angles & Triangles
Angle Quest Worksheet
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Date:
Period:
Parallel Transversals Alt. Int./Ext. & Corr. angles are equal (\(\cong\)). Same-Side Int. sum to \(180^\circ\).
Triangle Angle Sum The 3 interior angles sum to \(180^\circ\): \(m\angle A + m\angle B + m\angle C = 180^\circ\).
Exterior Angle Theorem Exterior angle equals sum of two remote interior angles: \(m\angle \text{ext} = m\angle 1 + m\angle 2\).
1 Part 1: Transversal Angle Relationships
Given line \(m \parallel n\) intersected by transversal \(t\)
m n t 1 2 3 4 5 6 7 8 Arrows indicate line \(m \parallel n\)
1 If \(m\angle 1 = 124^\circ\), find \(m\angle 5\) and state relationship:
Relationship:
\(m\angle 5 =\)
2 If \(m\angle 4 = 56^\circ\), find \(m\angle 5\) and state relationship:
Relationship:
\(m\angle 5 =\)
3 If \(m\angle 3 = (3x + 18)^\circ\) and \(m\angle 6 = (5x - 22)^\circ\), solve:
Work:
\(x =\)
\(m\angle 3 =\)
4 If \(m\angle 3 = (4x + 10)^\circ\) and \(m\angle 5 = (2x + 20)^\circ\), solve for \(x\):
Equation:
\(x =\)
2 Part 2: Triangle Angle Sum Theorem
Show all work clearly
5 Question 5
Find \(x^\circ\)
\(68^\circ\) \(47^\circ\) \(x^\circ\)
- Find the value of \(x\) and classify the triangle by its angles:
\(x =\) Type:
6 Question 6
Right \(\triangle\)
\(90^\circ\) \((2y+6)^\circ\) \(42^\circ\)
- Solve for \(y\) and determine the measure of the acute top angle:
\(y =\) Top \(\angle =\)
7 Question 7
Algebraic
\(50^\circ\) \((2x+20)^\circ\) \((3x+10)^\circ\)
- Given the \(50^\circ\) base angle, solve for \(x\) and both unknown angles:
\(x =\) Angles:
Geometry Practice: Parallel Lines & Triangle Angles Page 1 of 2 • Continue to Page 2 →
Part 3 & Part 4
Exterior Angles & Multi-Step Synthesis
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3 Part 3: Triangle Exterior Angle Theorem
Theorem: \(m\angle \text{ext} = m\angle \text{remote}_1 + m\angle \text{remote}_2\)
8 Question 8
Direct Exterior
\(58^\circ\) \(67^\circ\) \(d^\circ\)
- Given remote angles \(58^\circ\) and \(67^\circ\), use the exterior angle theorem to calculate \(d^\circ\):
Calculation:
\(d =\)
9 Question 9
Remote Interior
\(132^\circ\) \(49^\circ\) \(k^\circ\)
- Given exterior angle \(132^\circ\) and remote angle \(49^\circ\), solve for \(k^\circ\):
Equation:
\(k =\)
10 Question 10
Algebra & Ext.
\((2x+8)^\circ\) \(52^\circ\) \((5x-15)^\circ\)
- Given remote angle \(52^\circ\), solve for \(x\) and calculate the exterior angle:
\(x =\) Ext \(\angle =\)
4 Part 4: Transversal & Triangle Fusion Challenge
Apply multiple theorems in sequence
\(L_1\) \(L_2\) \(48^\circ\) \(62^\circ\) \(a\) \(b\) \(c\) \(d\)
Lines \(L_1 \parallel L_2\). Straight line across top apex and bottom base.
Find each angle measure in order. State the geometric justification:
\(m\angle a =\)
Reason:
\(m\angle b =\)
Reason:
\(m\angle c =\)
Reason:
\(m\angle d =\)
Reason:
11. Mathematical Reflection: Identify two distinct geometric theorems you could use to calculate \(m\angle d\). Briefly justify why both yield the identical value.
Geometry Practice: Triangle Exterior Angles & Transversal Systems Page 2 of 2 • End of Worksheet
