Calculating Interior Angles of a Trapezium
Published:
Work out the size of
a) angle TUV.
b) angle VWT.
This question includes visual content: A quadrilateral TUVW is shown. The sides TW and UV are parallel, indicated by arrowheads on the lines. Interior angle WTU is labeled as $102^\circ$. Interior angle UVW is labeled as $59^\circ$. The vertices are labeled U (top right), V (bottom right), W (bottom left), and T (top left). A note at the bottom states 'Not drawn accurately'.
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Step by Step Written Solution
Let's work out the size of the missing angles in this quadrilateral. We are given angle U T W is one hundred and two degrees, and angle U V W is fifty-nine degrees.
Angle Geometry Problem
Notice the arrowheads on lines T W and U V. These indicate that the lines are parallel to each other.
Key Finding: $TW \parallel UV$
First, let's find angle T U V. Because lines T W and U V are parallel, the angles T U V and U T W are co-interior angles, also known as allied angles.
Part a) Finding Angle TUV
Co-interior angles between parallel lines sum to one hundred and eighty degrees. So, we can set up an equation.
Subtracting one hundred and two from both sides, we find that angle T U V is seventy-eight degrees.
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