In the daigram AB ia parallel to CD, and AE is parallel to BC. AB=AC, angle ACD=68° and CDE=110° Find the size of the angle p ,q and r

p = 68° , q = 44° , r = 114°

Step-by-step explanation:

∠ ACD = ∠ BAC = p ( alternate angles ) so

p = 68°

Since AB = AC then Δ ABC is isosceles with base angles congruent, that is

∠ BCA = ∠ CAB = 68°

The sum of the 3 angles in the triangle = 180° , then

68° + 68° + q = 180°

136° + q = 180° ( subtract 136° from both sides )

q = 44°

∠ EAC = ∠ ACB ( alternate angles ) so

∠ EAC = 68°

The sum of the 4 angles in quadrilateral ACDE = 360°

r + 68° + 68° + 110° = 360°

r + 246° = 360° ( subtract 246° from both sides )

r = 114°

good luck on your studies! : )

david edward.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.