How am I supposed to find the measurements of angles B and C? Thanks in advance!

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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To solve this problem, split the shape in half by drawing line BD.

Now we have triangle ABD and we know that AB=AD (given)

Therefore `/_B_(1)=/_D_(1)` (isosceles triangle)and we are given that angle A=90.

Therefore, as the angles of a triangle =180 deg and A = 90 deg

Therefore   `/_B_(1) =/_ D_(1)=45 deg` 

We also know that triangle BCD is isosceles as BC=CD

`therefore`  `/_B_(2)=/_D_(2)` and we know that angle D=65(given)

We have already calculated `D_(1)=45 deg`

`therefore /_D_(2) = 65-45 = 20 therefore /_B_(2)=20`

As the angles of a triangle = 180:`/_C= 180 - 20 -20=140`

Ans: Angle B= 65 deg and Angle C=140 degrees.





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