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astra-53 [7]
3 years ago
11

Triangle MNO is similar to triangle PQR. If angle N measures 85 degrees and angle P measures 75 degrees, what is the measure of

angle R? 20 75 85 160
Mathematics
2 answers:
Eva8 [605]3 years ago
5 0
I think the answer is going to be 20
charle [14.2K]3 years ago
4 0

Answer:

The measure of angle R is 20°.

Step-by-step explanation:

Since, We know that,

When two triangles are similar then their corresponding angles are congruent or the measures of corresponding angles are equal,

In triangles MNO and PQR,

Angles M, N and O are corresponding to angles P, Q and R.

Given,

\triangle MNO\sim \triangle PQR

m\angle N=85^{\circ}

m\angle P=75^{\circ}

Also, By the above property,

m\angle N = m\angle Q

\implies m\angle Q = 85^{\circ}

Now, the sum of all interior angles of a triangle is supplementary,

So, in ΔPQR,

m\angle P+m\angle Q+m\angle R= 180^{\circ}

75^{\circ}+ 85^{\circ}+m\angle R= 180^{\circ}

160^{\circ}+m\angle R= 180^{\circ}

\implies m\angle R=20^{\circ}

Hence, the measure of angle R is 20°.

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