Mathematics
Grade 7
15 min
Find missing angles in triangles and quadrilaterals
Find missing angles in triangles and quadrilaterals
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1
Introduction & Learning Objectives
Learning Objectives
Identify interior angles in triangles and quadrilaterals.
Recall and apply the sum of interior angles rule for triangles.
Recall and apply the sum of interior angles rule for quadrilaterals.
Use algebraic equations to solve for unknown angles.
Solve problems involving missing angles in composite figures or figures with angles on a straight line.
Distinguish between different types of angles (e.g., acute, obtuse, right) within these figures.
Ever wonder how builders or designers make sure corners fit perfectly? 📐 It's all about understanding angles!
In this lesson, you'll learn the fundamental rules for angles inside triangles and quadrilaterals. Mastering these rules will allow you to find any missing angle, which is a crucial skill in geometr...
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Key Concepts & Vocabulary
TermDefinitionExample
AngleThe space between two intersecting lines or surfaces at or close to the point where they meet.In a square, each corner forms a 90-degree angle.
VertexThe common endpoint of two or more rays or line segments, forming an angle.The point where two sides of a triangle meet is a vertex.
TriangleA polygon with three sides and three angles.A slice of pizza is often a triangle.
QuadrilateralA polygon with four sides and four angles.A window pane or a TV screen is typically a quadrilateral (rectangle).
Interior AngleAn angle inside a polygon, formed by two adjacent sides.The angles at the corners of a rectangle are all interior angles.
Supplementary AnglesTwo angles whose sum is 180 degrees. They often form a straight line.If one angle on a straight line is 60 degrees, t...
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Core Formulas
Sum of Angles in a Triangle
$A + B + C = 180^\circ$
Use this rule when you know two angles of a triangle and need to find the third.
Sum of Angles in a Quadrilateral
$A + B + C + D = 360^\circ$
Apply this rule when you know three angles of a quadrilateral and need to find the fourth.
Angles on a Straight Line (Linear Pair)
$x + y = 180^\circ$
Useful when an angle inside a figure is adjacent to an angle outside the figure, and they form a straight line.
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Challenging
A quadrilateral ABCD and a triangle ADE share vertex D. The points A, D, and C are on a straight line. In the quadrilateral, angle B = 120° and the other three angles (A, C, and D) are equal to each other. What is the measure of angle ADE?
A.80°
B.90°
C.100°
D.120°
Challenging
A quadrilateral ABCD is split by a diagonal AC. In triangle ABC, angle BAC = 25° and angle B = 110°. In triangle ADC, angle ACD = 35° and angle D = 80°. What is the measure of the complete angle BCD?
A.45°
B.70°
C.115°
D.80°
Challenging
In triangle ABC, the exterior angle at vertex C is 130°. A point D is on the side AC. If angle BDC is 100°, what is the measure of angle DBC?
A.40°
B.30°
C.50°
D.60°
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