Video: Pack 3 β€’ Paper 1 β€’ Question 3

Pack 3 β€’ Paper 1 β€’ Question 3

01:42

Video Transcript

𝐴𝐡𝐢 is parallel to 𝐹𝐺𝐻. And 𝐹𝐷𝐡 is parallel to 𝐺𝐸𝐢. 𝐺𝐸 is equal to 𝐸𝐻. Angle 𝐼𝐻𝐽 is equal to 44 degrees. Work out the size of the angle marked π‘₯. You must give reasons for your answer.

Angle 𝐸𝐻𝐺 is equal to angle 𝐼𝐻𝐽, as opposite angles are equal. Therefore, angle 𝐸𝐻𝐺 is 44 degrees. We were told in the question that 𝐺𝐸 is equal to 𝐸𝐻. Therefore, triangle 𝐺𝐸𝐻 is isosceles.

As the triangle is isosceles, we know that two angles will be equal. In this case, angle 𝐸𝐻𝐺 is equal to angle 𝐻𝐺𝐸. They are both equal to 44 degrees. Finally, angles 𝐻𝐺𝐸 and 𝐡𝐢𝐸 are also equal. This is because they are alternate angles or 𝑍 angles.

As 𝐴𝐡𝐢 is parallel to 𝐹𝐺𝐻, we can draw letter 𝑍 to show that these two angles are equal. Using the angle properties of opposite angles, alternate angles, and the angles in an isosceles triangle, we’ve proved that π‘₯ is equal to 44 degrees.

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