Isosceles triangle angles Practice Questions (Grade 8)

Question 1easy

In $\triangle PQR$ , $\angle P$ and $\angle Q$ are congruent. The measure of $\angle R$ is $118.6^{\circ}$ . What is the measure of $\angle Q$ ?

Let each congruent angle measure $x^{\circ}$ . Then $2x + 118.6 = 180$ , so $x = \dfrac{180 - 118.6}{2} = 30.7^{\circ}$ .

Question 2easy

In $\triangle XYZ$ , $\angle X$ and $\angle Z$ are congruent. The measure of $\angle Y$ is $52.6^{\circ}$ . What is the measure of $\angle X$ ?

The two congruent angles share the remainder equally: $\dfrac{180^{\circ} - 52.6^{\circ}}{2} = 63.7^{\circ}$ .

Question 3easy

In $\triangle ABC$ , $\angle B$ and $\angle C$ are congruent. The measure of $\angle A$ is $124.8^{\circ}$ . What is the measure of $\angle C$ ?

Each congruent angle is $\dfrac{180^{\circ} - 124.8^{\circ}}{2} = 27.6^{\circ}$ .

Question 4easy

In $\triangle RST$ , $\angle R$ and $\angle T$ are congruent. The measure of each of these angles is $43.9^{\circ}$ . What is the measure of $\angle S$ ?

The congruent angles total $2 \times 43.9^{\circ} = 87.8^{\circ}$ , so $\angle S = 180^{\circ} - 87.8^{\circ} = 92.2^{\circ}$ .

Question 5medium

In $\triangle LMN$ , $\angle L$ and $\angle N$ are congruent. Each of these angles measures $38.2^{\circ}$ . What is the measure of $\angle M$ ?

Together the congruent angles measure $2 \times 38.2^{\circ} = 76.4^{\circ}$ , so $\angle M = 180^{\circ} - 76.4^{\circ} = 103.6^{\circ}$ .

Question 6medium

In $\triangle GHI$ , $\angle G$ and $\angle I$ are congruent. The measure of $\angle H$ is $88.4^{\circ}$ . What is the measure of $\angle G$ ?

Each congruent angle is $\dfrac{180^{\circ} - 88.4^{\circ}}{2} = 45.8^{\circ}$ .

Question 7medium

In $\triangle JKL$ , $\angle J$ and $\angle L$ are congruent. The measure of each of these angles is $61.7^{\circ}$ . What is the measure of $\angle K$ ?

The two congruent angles total $2 \times 61.7^{\circ} = 123.4^{\circ}$ , so $\angle K = 180^{\circ} - 123.4^{\circ} = 56.6^{\circ}$ .

Question 8medium

In $\triangle MNO$ , $\angle M$ and $\angle O$ are congruent. The measure of $\angle N$ is $105.2^{\circ}$ . What is the measure of $\angle M$ ?

Each congruent angle is $\dfrac{180^{\circ} - 105.2^{\circ}}{2} = 37.4^{\circ}$ .

Isosceles triangle angles practice

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