/* Base Styles (Mobile First) */
.r-container {
font-family: ‘Inter’, Arial, sans-serif;
color: #515151;
max-width: 1300px;
margin: 0 auto;
}
.r-section {
padding: 40px 20px;
}
.r-section-title {
font-size: 2.2em;
color: #00463a;
margin-top: 0;
margin-bottom: 30px;
font-weight: 700;
line-height: 1.2;
text-align: center;
}
.r-section-subtitle {
font-size: 1.2em;
max-width: 800px;
margin: 0 auto 30px auto;
line-height: 1.7;
text-align: center;
}
.r-faq-grid {
max-width: 800px;
margin: 0 auto;
display: grid;
gap: 20px;
}
.r-faq-item {
background-color: #f7f6f5;
border-left: 6px solid #92d0ff;
padding: 20px 25px;
border-radius: 16px;
}
.r-faq-question {
font-size: 1.15em;
margin-top: 0;
font-weight: 600;
color: #00463a;
}
.r-faq-answer {
line-height: 1.7;
font-size: 1.1em;
margin-bottom: 0;
}
.r-grid {
display: grid;
grid-template-columns: 1fr;
gap: 20px;
max-width: 1100px;
margin: 0 auto;
}
.r-card {
background-color: #ffffff;
padding: 25px;
border-radius: 16px;
}
.r-card h3 {
font-size: 1.5em;
color: #00463a;
margin-top: 0;
}
.r-card p, .r-card li {
line-height: 1.6;
font-size: 1.1em;
}
.r-card ol { padding-left: 20px; }
.r-details {
background-color: #f7f6f5;
border-radius: 16px;
margin-top: 30px;
}
.r-details summary {
font-weight: 700;
font-size: 1.2em;
color: #00463a;
padding: 20px;
cursor: pointer;
}
.r-details-content {
padding: 0 20px 20px 20px;
border-top: 1px solid #d1d1d1;
}
/* Desktop Styles */
@media (min-width: 768px) {
.r-section {
padding: 60px 40px;
}
.r-section-title {
font-size: 2.5em;
}
.r-section-subtitle {
font-size: 1.3em;
}
.r-grid.two-col {
grid-template-columns: repeat(2, 1fr);
}
}
Angle Facts
Understanding how angles behave around points, on straight lines, and with parallel lines is a fundamental skill in geometry. These key angle facts help engineers design bridges, architects plan buildings, and are essential for solving a huge range of problems in your GCSE Maths exam.
Key Angle Facts to Remember
Angles at a Point
Angles that meet at a single point and make a full turn always add up to $360^\circ$.
Angles on a Straight Line
Angles that sit on a straight line and share a common vertex always add up to $180^\circ$.
Vertically Opposite Angles
When two straight lines cross, the angles directly opposite each other are equal. Vertically opposite angles always have the shape of ‘X’ as they have the ‘X’ shape
Angles in Parallel Lines
When a line (transversal) crosses two parallel lines:
- Alternate angles (Z-shape) are equal.
- Corresponding angles (F-shape) are equal.
Worked Examples
Example 1: Vertically Opposite Angles
Find the size of angles $a$ and $b$. Give reasons.
- $a = 55^\circ$ (Vertically opposite angles are equal).
- $b + 55^\circ = 180^\circ$. So, $b = 125^\circ$ (Angles on a straight line add up to $180^\circ$).
Example 2: Angles in Parallel Lines
Find the size of angles $x$ and $y$. Give reasons.
- $x = 70^\circ$ (Alternate angles are equal – look for the ‘Z’ shape).
- $y + 70^\circ = 180^\circ$. So, $y = 110^\circ$ (Angles on a straight line add up to $180^\circ$).
Tutor Insights
🤔 Common Misunderstandings
- Assuming lines are parallel. You can only use alternate or corresponding angle rules if the lines are marked with arrows to show they are parallel.
- Mixing up alternate and corresponding angles. Using the ‘Z’ and ‘F’ shapes is a great way to remember which is which.
📝 Common Exam Mistakes
- Not giving reasons. You must state the full angle fact (e.g., “Angles on a straight line add up to $180^\circ$”) to get full marks.
- Calculation errors when subtracting from 180 or 360.
- One-step thinking. Forgetting that a problem might require two or three steps to solve.
Practice Questions
- Find the value of $x$, giving a reason for your answer.
130°x
- Find the values of $a$ and $b$, giving reasons for your answers.
ab40°
Show Answers
- $x = 50^\circ$.
Reason: Angles on a straight line add up to $180^\circ$. ($180 – 130 = 50$). - $a = 40^\circ$.
Reason: Vertically opposite angles are equal.
$b = 140^\circ$.
Reason: Angles on a straight line add up to $180^\circ$. ($180 – 40 = 140$).
