ABCD is a trapezium. ∠p=∠q\angle p = \angle q. Find the sum of ∠r\angle r and ∠s\angle s. Ans : _______________ ∘^\circ

Work through it with AI →

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

3

1. Find $\angle p$ using angles at a point

∠p=360∘−302∘=58∘\angle p = 360^\circ - 302^\circ = 58^\circ

2. Find $\angle q$ using the given condition

Since ∠p=∠q\angle p = \angle q, we have ∠q=58∘\angle q = 58^\circ.

3. Find the sum of $\angle r$ and $\angle s$ using the angle sum of a triangle

In △ADE\triangle ADE, the sum of angles is 180∘180^\circ.
∠r+∠s+∠q=180∘\angle r + \angle s + \angle q = 180^\circ
∠r+∠s=180∘−58∘=122∘\angle r + \angle s = 180^\circ - 58^\circ = 122^\circ

Answer

122122

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.

More questions on this topic

  1. 1In the figure, WXYZ is a trapezium and AXYB is a rhombus. XBC and XAZ are straight lines. WX // ZY, BC = BY, ∠XAB=82∘\angle XAB = 82^\circ…
  2. 2In the figure below, ABCD is a trapezium. AF and EC are straight lines. Peishan wrote four statements to describe the fi…
  3. 3In the figure below, ABGF and BCDG are rhombuses. ∠ABF=31∘\angle ABF = 31^\circ, ∠CBG=40∘\angle CBG = 40^\circ and EF is parallel to…
  4. 4In the figure, PQ = PS and SRP is a straight line. Find ∠RQS\angle\text{RQS}. Ans: ___ ∘^\circ
  5. 53.76°= 度 分 秒.