Sides of similar triangles

Question

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In the attached question, I am able to find x but not y. I know that sides of similar triangles are proportionate but that's not helping here. And I guess the third side of the smaller tringle would be (y+3)/2 but how to calculate y?

X would 68 degrees as it is opposite to the propotionate side y+3. (corresponding angles of similar triangles are equal).

Wouldn't the angle at B be the same as the angle at P and thus 68° ? — JohanC, Jan 13 '20 at 19:51
My bad. Didn't use proper logic. But still not able to see why P equals B and not A. — aarbee, Jan 13 '20 at 19:58

Quanto · Answer 1 · 2020-01-13T20:17:19.653

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Note that B = P = 68 and $x$ = 180 - 54 - 68 = 58. The similar triangles leads to the ratio

$$\frac{y+3}{2y}=\frac y {y+2}$$

Edit: There may some issue with the problem. Either B is 68 or 58 would mean y > y + 2, which is not true.

edited Jan 13 '20 at 20:17

answered Jan 13 '20 at 19:52

Quanto

97,352

Sorry, why P equals B and not A? – aarbee Jan 13 '20 at 19:56
@Ramit - A=P is impossible, which would mean B=58>54 and y>y+2. – Quanto Jan 13 '20 at 20:00
If B is 68, and 68>54 i.e. y>y+2? (just trying to understand) – aarbee Jan 13 '20 at 20:07
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@Ramit - you're right. both are unlikely. Some is off with the problem. – Quanto Jan 13 '20 at 20:13

Sides of similar triangles

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